5.09 Module 5 Review

05.09 Module Five Review and DBA
05.01 Four Phases of Matter * Matter exists in different phases, also called states, which include solid,liquid, gas, and plasma. These phases can be distinguished at the molecular level by how the particles are held together. * Solids * In the solid phase, the intermolecular attraction between particles of matter is strong enough to hold all the particles together in a fixed three-dimensional arrangement. Because of the rigid arrangement of particles, solids retain both their shape and volume. * Remember that temperature is a measure of the average kinetic energy of the particles in a substance. This means that the addition of heat to a solid causes the vibration of the particles to increase more and more as the temperature of the solid increases. This increase in vibration will continue until, at a certain temperature, the vibrations are rapid enough to break up the fixed arrangement of particles. At this point a solid will begin to melt into a liquid. * Shape: definite * Volume: definite * Liquids * In the liquid phase, the particles can move past each other. The kinetic energy of the particles in a liquid is high enough to partially overcome the intermolecular attraction between the particles, but the attraction is still strong enough to hold the particles close together. This allows liquids to flow instead of being held together in a rigid structure. * Heating a liquid causes the particles to move faster and faster as temperature increases. Eventually, the particles will flow so fast that the attractions they have for each other are unable to hold them together. At this point, a different temperature for different substances, the particles will separate from each other and will reach the gas phase. * Shape: not definite * Volume: definite * Gas * The particles of a gas have a high amount of kinetic energy, so they are moving fast enough to completely overcome the intermolecular forces of attraction between them. This means that the particles can move independently of each other, moving in random directions and filling the entire container in which they are held. * Gases do not have a definite shape or volume. With the high speed and random motion, gas particles spread out to fill whatever container they are in. Because of the large amount of space between the particles, gases can be condensed to smaller volumes when pressure is applied. If you decrease the pressure exerted on a gas, like when you open the valve on an oxygen gas tank to release the oxygen, the gas expands to a greater volume. * When enough energy is added to a gas to raise it to an extreme temperature, over 5,000°C, the particles will have so much kinetic energy that the movement and collisions will break electrons out of the atoms. When the electrons have been forced off of the atoms because of these extreme conditions, the particles will reach the plasma phase. * Shape: not definite * Volume: not definite * Plasma * Plasma is described as an electrically charged gas. Because of extreme temperatures, the particles move so quickly that their collisions release electrons from the atoms. This mixture of electrons and positively charged ions with high kinetic energy is described as the plasma phase. * Because of its extreme temperature, plasma is not common on Earth. We will not encounter the plasma phase in this course’s chemistry lab investigations. The sun and other stars are made of elements in the plasma state, and plasmas can also be found inside of a glowing fluorescent light bulb, the small fluorescent lights in plasma television screens, and at locations where high-energy lightning strikes in the air. * 05.02 Phase Changes * Melting * Melting is the process of a solid transforming to a liquid. When heat is added to a solid, the particles’ kinetic energy increases and they vibrate more and more violently. If enough heat is added, the attractive forces between the particles are not able to hold them together. This is when the solid melts, and the temperature at which a given substance melts is called its melting point. * Freezing * Freezing is the process of transforming a liquid to a solid by the removal of heat, the reverse of the melting process. As the sample of liquid loses heat, the particles’ movement slows down. The particles continue to move slower and slower until the attractive forces between them are able to hold the particles in a fixed position, transforming the liquid into a solid. The only motion the particles have as a solid is a vibration within their fixed positions. The temperature at which a given substance transforms from a liquid to a solid is called its freezing point, which is the same temperature as the substance’s melting point. * Evaporating * The process of transforming a liquid to a gas is called evaporating. As heat is added, the particles in the liquid have a greater kinetic energy and move faster. Particles at the surface of the liquid eventually have enough kinetic energy to escape the liquid phase and become a gas. As more particles absorb the heat being added, they also move fast enough to transfer to the gas phase. A gas can also be called vapor, related to the word evaporation, which means that the process of becoming a gas can also be called vaporization. * It requires about seven times as much energy to vaporize a sample of water (transfer it from the liquid to gas phase) as it does to melt the same amount of water (transfer from the solid to liquid phase). The rate of evaporation of a liquid increases with temperature. * When the temperature is high enough, evaporation occurs from within the sample of liquid instead of just at the surface. We call this process boiling. Chemists identify the boiling point of a substance, the temperature at which a substance boils, as one of its physical properties. * Condensing * The process of transforming a gas to a liquid is called condensing, the opposite of evaporation. This process occurs when the temperature of the gas is cooled enough for the particles to slow down and attract each other, forming a liquid. The temperature at which this phase change occurs is called the condensation point, the same temperature as the substance’s boiling point. * Did You Know? * The dew point is the temperature at which the water vapor in the air will condense to a liquid. The dew point for a given day depends on the atmospheric pressure and other factors, so it may be different from day to day and season to season for your area. * Water can exist in three states (or three phases): * Solid phase: The particles in a solid are strongly bonded to one another. Ice cubes maintain their form regardless of the container that holds them. * Liquid phase: The particles are no longer in an ordered state. The bonds between molecules are broken, and the liquid water takes the shape of its container. The particles are very close to one another, and so a liquid is incompressible. * Gaseous phase: Agitation and disorder are at the maximum level. Water vapor occupies all of the space in a container. The distances between molecules are large. A gas is compressible. * A heating curve: it represents the change in temperature as a substance under constant heat changes from a solid to a liquid to a gas. Solid | Solid-Liquid
Phase Change | Liquid | Liquid-Gas
Phase Change | Gas | −40–0 (°C) | 0 (°C) | 0–100 (°C) | 100 (°C) | 100–130 (°C) | | melting point | | boiling point | | * What does the second horizontal section of the heating curve represent? This flat section of the graph represents the substance’s boiling point. When the liquid begins to boil, the temperature remains constant as the heat energy provided by the flame is used to move the particles farther apart to change the liquid to a gas. * A cooling curve: shows the temperature change as a substance loses energy and cools down. Cooling curves have the same horizontal sections that you saw in heating curves, where the phase changes from a gas to a liquid or from a liquid to a solid. Gas | Gas-Liquid
Phase Change | Liquid | Liquid-Solid
Phase Change | Solid | 130–100 (°C) | 100 (°C) | 100–0 (°C) | 0 (°C) | 0–−40 (°C) | | condensation point | | freezing point | | * 05.03 Gas Laws * Robert Boyle (1627-1691), an Irish born scientist, made many contributions to science through his study of gases. In 1661, he published "The Sceptical Chymist." In it, he argued that Aristotle's view of matter being made of four elements, fire, earth, air and water was incorrect. He proposed that matter was made of particles called atoms which moved around. Physical Characteristics and Variable | Typical Units | Volume (V) | Liters (L) | Pressure (P) | Atmosphere (atm) | Temperature (T) | Kelvin (K) | Number of particles (n) | Moles (mol) | Ideal gas constant, R | * x atm / K mol | * The SI unit of pressure is the Pascal (Pa), which is defined as one newton per square meter(N/m2). However, chemists most often use units of atmospheres (atm) or millimeters of mercury (mm Hg) to measure pressure. Units of Pressure | 1 atmosphere (atm) | = 760 mm Hg | | = 760 torr | | = 101.3 kilopascals (kPa) | * 785 mm Hg = ? atm * 785 mm Hg × 1 atm / 760 mm Hg = 1.03 atm * Temperature Conversions * When you want to convert from Celsius to Kelvin * K= 273.15 + oC * When you want to convert Kelvin to Celsius * oC= K-273.15 * The Nature of Gases * Low Density * The density of a substance in the gas phase is about 1/1,000 the density of the same substance as a liquid because the gas particles spread out so much farther from each other than they do as a liquid. * Compressibility * When enough pressure is applied, gases can be compressed to a smaller volume because there is so much space between the particles. With enough pressure, a gas can sometimes be compressed to a volume thousands of times smaller than its initial volume. * Expansion * Gases spread out to fill the entire container in which they are enclosed because the gas particles are moving in all directions with negligible attractive forces between them. This means that a gas transferred from a 2-liter container to a 4-liter container will expand, or spread out, to fill the entire 4-liter container. * Diffusion * Because of their high kinetic energy and random motion, gas particles can spread out and mix with each other without being stirred. The scent of ammonia travels through a room as its gas particles mix with the particles of air. * Fluidity * Gas particles are able to easily glide, or flow, past each other because the attractive forces between them are negligible. The term fluid is sometimes used to describe both liquids and gases because of their ability to flow. * The Kinetic Molecular Theory of Gases * The kinetic molecular theory of gases provides a model of an ideal gas that helps us understand the properties and behaviors of gas particles. An ideal gas is an imaginary gas that behaves according to all of the assumptions of the kinetic molecular theoryThe particles of a gas are in constant random motion. * The particles of a gas are in constant random motion. * Gases consist of large numbers of tiny particles. * The collisions experienced by gas particles are elastic collisions. * There are no forces of attraction or repulsion experienced between gas particles. * The average kinetic energy of the particles of a gas is directly proportional to the temperature, in Kelvin, of the gas. * Gas Laws * The pressure and volume of a sample of gas have an inverse relationship; as one of these values increases, the other decreases (and vice versa). This relationship is represented by the gas law known as Boyle's law, which compares an initial pressure and volume to a final pressure and volume when temperature and number of moles are held constant. * Boyle's law: P1V1 = P2V2

* Where P1 = initial pressure, V1 = initial volume, P2 = final pressure, V2 = final volume * Temperature and pressure are directly related to each other, meaning that when one increases, so does the other, and vice versa. This relationship between temperature and pressure is represented by Gay-Lussac's law. This formula shows the direct relationship between the temperature and pressure of a gas and allows you to make predictions using this relationship, as long as volume and moles remain constant. * Gay-Lussac's law: = P1 / T1 = P2 / T2 * Where P1 = initial pressure, T1 = initial temperature, P2 = final pressure, T2 = final temperature * Temperature and volume are directly related to each other. An increase in the temperature of a gas means an increase in the average kinetic energy of the gas particles. As the temperature increases, the particles move faster. If the container is flexible, like a balloon, then the container will expand so that the pressure (and number of collisions) inside the container remain constant. This is why gases expand when heated and contract when cooled. * Charles's law: = V1 / T2 = V2 / T2 * Important note: The relationship represented by Charles's law is only valid if temperature is represented in the unit Kelvin, so there are no negative temperature values. * Moles of gas particles and volume are directly related. This means that as one increases, so does the other, and if one decreases, so does the other. This relationship between volume and moles is represented by Avogadro's law. * Avogadro's law: V1 / n1 = V2 / n2 * The number of gas particles (moles) and pressure are directly related; as one property increases, so does the other. Pressure gauges make use of this direct relationship when they are used to estimate the amount of gas left in an oxygen or helium tank. * 05.04 Gas Calculations * Ideal gas law: PV = nRT * The new variable in this equation, R, represents a constant known as the ideal gas constant. Its value depends on the units being used for pressure, volume, moles, and temperature. * R = 0.0821 L atm / mol K * We will use the above value of the ideal gas constant as long as volume (V) is in the unit liters, pressure (P) is in atmospheres, temperature (T) is in kelvin, and (n) is in moles. * Although the general setup for the ideal gas law is given as PV = nRT, this equation can be rearranged to solve for any of the four properties (P, V, n, or T) of a gas. Solving for | Typical Units | Pressure (in atmospheres): | P = nRT / V | Volume (in liters): | V = nRT / P | Temperature (in kelvin): | T = PV / nR | Number of Particles (in moles): | n = PV / RT | * Mole Ratios and Coefficients * We have already seen that the coefficients in a balanced equation represent a mole ratio between the reactants and products. If the entire reaction occurs at a constant temperature and pressure, then Avogadro’s law tells us that volume and moles are directly related, no matter the identity of the gas. * Because of the relationships between volume and moles, the coefficients in a balanced equation can represent a volume ratio whenever pressure and temperature remain constant throughout the reaction. This means that you can convert from volume of one gaseous reactant or product to the volume of another by using the coefficients as a volume ratio. * 2 CO(g) + O2 (g)→ 2 CO2 (g) * The coefficients in this balanced equation provide a volume ratio between gases when they are all at the same temperature and pressure. * A given volume of oxygen gas will react with twice that volume of carbon dioxide, because the ratio of O2 to CO is 1:2 (given by the coefficients). * The coefficients provide volume ratios (only for gaseous reactants and products) that can be used in stoichiometry calculations involving volume. * Standard Temperature and Pressure * To aid in the comparisons of volumes or moles of gases, scientists have agreed upon conditions known as standard temperature and pressure, commonly abbreviated STP. The conditions of standard temperature and pressure are exactly one atmosphere pressure and 0°C (273.15 Kelvin). * Avogadro’s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. At standard temperature and pressure (STP), one mole of any gas occupies a volume of 22.4 liters. This mole-to-volume relationship can be used as conversion factor in calculations pertaining to measurements and reactions conducted at STP (1 atmosphere and 273.15 Kelvin). Standard temperature and pressure | (STP) | 1 standard temperature | 0°C | 1 standard temperature | 273 K | 1 standard pressure | 1 atm | 1 standard pressure | 760 torr | 1 standard pressure | 14.7 psi | * At 1 atm and 273.15 K * 1 mole of gas / 22.4 L or 22.4 L / 1 mole of gas * These ratios can be used within a stoichiometry calculation whenever the conditions are at STP. This relationship between volume and moles replaces the need to use the ideal gas law. * Diffusion and Effusion * The constant motion of gas particles causes them to spread out and fill any container in which they are placed. When two gases gradually mix together because of this random motion, it is called diffusion. A similar term, effusion, describes when a gas sealed in a container with a small hole gradually leaks out of the hole as the motion of the gas particles results in the particles randomly encountering, and passing through, the hole. * Speed is related to mass, the greater the mass the slower the speed of the particles. * Graham's Law * Rate of effusion A / rate of effusion of B = square root molar mass B /square root molarA * This equation shows that the rate at which two different gases (A and B) effuse from the same container is dependent on their molar masses. Notice that in the equation the molar mass of A is diagonal from the rate of A. Also notice that to actually calculate and compare the rates of effusion, the square root of each molar mass must be taken. * 5.05 Mixtures and Solutions * All matter can be classified into two categories: pure substances and mixtures. We have already explored pure substances quite a bit in this course. A pure substance is a sample of matter that is made up of one type of element or compound. Pure gold metal is formed only of gold (Au) atoms; table salt is formed only of sodium chloride (NaCl) molecules. * A mixture: is a combination of two or more substances, elements, or compounds, in which each substance retains its own individual properties. This means that in a mixture, the different substances are not bonded together like the atoms in a compound. * When a compound is formed, it has different chemical and physical properties than the pure elements it is made of, and it can only be separated by a chemical change. * In a mixture, the individual substances retain their own properties and can be separated easily by physical means. Refer to the table below to see a comparison of compounds and mixtures. | Mixture | Compound | Composition | Varied composition—you can vary the amount of each of the substances in a mixture. | Definite composition—the atoms are bonded in specific ratios (given in the chemical formula). | Properties | Each substance in the mixture retains its own chemical and physical properties. | The compound has different properties than the elements it contains. | Bonding | The different substances are not chemically bonded together. | The different elements are chemically bonded together. | Separation | Each substance is easily separated from the mixture by physical means. | The compound can only be separated into its elements by a chemical change (reaction). | Examples | Air, most rocks and ores, salt water | Water, carbon dioxide, sodium chloride | * Homogeneous and Heterogeneous * Homogeneous * Homo: Same * Heterogeneous * Hetero: Different * In a heterogeneous mixture, the composition of the mixture is not uniform, or the same, throughout. * In a homogeneous mixture, the composition of the mixture is uniform throughout. * Homogeneous mixtures are also called solutions. Solutions can exist in solid, liquid, or gaseous states. * Separating Mixtures * Filtration: is a useful technique for separating an insoluble solid from a liquid. An insoluble substance is one that does not dissolve in the liquid. * Filtration is a common laboratory technique. Chemists can separate precipitates formed in chemical reactions from the aqueous solution in which they are formed using filtration. This is possible because precipitates are insoluble solids, so the precipitate will remain behind on the filter paper as the water and dissolved particles pass through the filter. * Evaporation: this is good for separating a soluble solid from a liquid (a soluble substance dissolves, to form a solution, so it cannot be separated using a filter). * Distillation: is a good technique for separating a liquid from a solution. For example, water can be separated from salty water by simple distillation. This works in the same way as the evaporation example, except that this technique captures the evaporated liquid and condenses it in a separate container. This method allows you to isolate the solute and the solvent each in a separate container. * Chromatography: is a group of lab techniques that are used to separate a solution containing multiple components with different degrees of polarity. A common type of chromatography, paper chromatography, takes place on a strip of porous, absorbent paper. * 05.06 Solubility and Concentrations * When we describe solutions, the component present in the largest amount is called the solvent, and any other components are called the solutes. * Universal Solvent * Water is often called the universal solvent, because a lot of different substances dissolve in water. Solutions in which water is the solvent are called aqueous solutions, labeled with the subscript (aq). Water is a polar molecule, which means it has a strong intermolecular force of attraction toward other polar molecules (including sugars, alcohols, and many other common substances) and ions (from table salt and other ionic compounds). * Cohesive Nature * Remember that water is a polar molecule that experiences hydrogen bonding between molecules, so the molecules of water have a strong attraction for each other. This strong attraction is what causes water molecules to cling together to form droplets, and it is also responsible for the surface tension of water. Surface tension is a property of liquids, caused by the attraction between molecules, which makes the surface less penetrable by solid objects. * Water and Ice * When most liquids freeze, the molecules pack together and move closer. Water is an exception. When water molecules freeze, they actually move farther apart. This makes frozen water (ice) less dense than liquid water, which is why ice floats. This property of water is important for the organisms living in large bodies of water, like lakes and ponds, where the water freezes in the winter. * Dissolving Process * If a solute is able to dissolve in a solvent, it does so because the attractive forces between the solute and solvent are as strong as, or stronger than, the intermolecular forces between the solute particles and between the solvent particles individually. * The solute particles become separated as the forces of attraction between them are disturbed. This step requires energy. * The solvent particles move apart as the forces of attraction between them are disturbed. This step requires energy. * The solvent particles begin attracting the solute particles, and they mix together as new attractive forces are formed. This step releases energy. * Saturation * At that point, the water is saturated with sugar, meaning the glass of water cannot accept any more solute at that temperature. * A solution that has not reached the point of saturation, meaning that more solute can still be added and dissolved, is called an unsaturated solution. * Factors Affecting Solubility * Even when substances mix well together, solubility can be increased or decreased by changes to temperature or pressure. * Dissolving a Solid * The solubility of a solid in a liquid increases with increasing temperature. With the increase in temperature, the kinetic energy of the solvent particles increases and the particles collide with the solid solute more vigorously. These collisions help break apart the solid, interfering with the attraction between the solute particles and allowing more of the solute to dissolve. * Dissolving a Gas * The effect of temperature on the solubility of a gas in a liquid is the opposite of how temperature affects the solubility of a solid. The solubility of a gaseous solute decreases with an increase in the temperature of the liquid solvent. With an increase in temperature, the solvent particles move faster. As the motion of the liquid particles increases, the gas solute particles come in contact with the surface more frequently, escaping from the solution more often. * Pressure * As we have already learned, the properties of gases are affected by pressure. This is also true for the solubility of a gas in a liquid solvent. A greater pressure above the surface of the liquid will increase the amount of gas able to be dissolved in that liquid. Decreasing the pressure above the solution will decrease the amount of gas able to be dissolved, which will result in some of the gaseous solute bubbling out of the solution. * Concentration * Molarity * Molarity (M): is a unit of concentration expressed in moles of solute per one liter of solution. This is a unit of concentration that is used a lot by chemists because it involves the mole, a unit that is common for expressing quantity. * Molarity (M) =

* 105 g NaCl × = 1.80 mol NaCl

* Molarity (M) =

* Molarity (M) =

* Molarity (M) = 0.514 M NaCl * Percent by Mass * The percent by mass of a solution: is the mass of solute (in grams) dissolved in a total of 100 grams of solution, expressed as a percentage. Notice that the numerator of the ratio is the mass of the solute alone, while the denominator is the mass of the solute plus the mass of the solvent to give the total mass of the solution. * Percent by mass (%) = × 100%

* or

* Percent by mass (%) = × 100%

* Percent by mass (%) = × 100%

* Percent by mass of CaCl2 = × 100%

* This solution is 10.7 % CaCl2 by mass.

* 05.07 Molarity and Dilution

* Solution Stoichiometry

* Mg (s) + 2 HCl (aq) → MgCl2 (aq) + H2 (g)

* 2.5 M HCl: This can be used as a conversion factor between moles of HCl and liters of HCl solution (). * 32.0 g Mg: This is the given amount of magnesium, which will be used to start the stoichiometry problem. * We are asked to solve for the volume of HCl solution (in milliliters). * Stoichiometry Set Up: * 32.0 g Mg × × × × = 1,050 mL of the HCl * Dilution * They can then dilute the stock solution by adding water until they have the exact concentration they need. * A stock solution is 28.2 percent ammonia (NH3) by mass, and the solution has a density of 0.8990 grams per milliliter. What volume, in milliliters, of this stock solution is required to prepare 600 milliliters of a 0.500 molar ammonia solution? * Diluted Solution: 600.0 mL volume, 0.500 M concentration * Stock Solution: 28.2% by mass, 0.8990 g/mL density, solve for volume in mL * Solve for Moles of Solute needed: * 600.0 mL NH3 solution (diluted) × × = 0.300 mol NH3 * Solve for the Volume of Stock Solution that Contains 0.300 moles of the Solute: * 0.300 mol NH3 solute × × × = 20.2 mL NH3 stock solution * 05.08 Colligative Properties * A colligative property: is a property of a solvent that depends on the number of solute particles dissolved in it, but not on the identity or nature of those solute particles. * Vapor Pressure * Vapor pressure: is the pressure exerted by the vapor particles that evaporate from a liquid (or solid). Vapor pressure can only be measured accurately when the evaporation occurs in a closed container. * As you increase the temperature of a liquid or solid, its vapor pressure also increases. On the other hand, vapor pressure decreases as the temperature of the liquid or solid decreases. * Vapor pressure of a solution * When a solute that does not evaporate well, it dissolves in a liquid to form a solution; the vapor pressure above that solution will be lower than the vapor pressure of the pure solvent. Remember that liquid particles at the surface of a liquid can escape to the gas phase when they have enough energy to break free of the liquid's intermolecular forces. * If we add solute particles to that liquid, the amount of surface area available for the escaping solvent molecules is reduced because some of that area is occupied by solute particles that are not able to evaporate. * Boiling Point * The boiling point: of a liquid is the temperature at which the vapor pressure of the liquid is equal to the atmospheric pressure of the surrounding air. Because the vapor pressure of a liquid is lowered by the addition of a dissolved solute, the solution will need to be heated to a higher temperature for its vapor pressure to equal the atmospheric pressure. This is why dissolving a solute in a solvent increases the boiling point. * Freezing Point * Every liquid has a freezing point, the temperature at which a liquid undergoes a phase change from liquid to solid. As the liquid particles slow down, the attraction between the particles causes them to form solid crystal structures that lock them in place in the solid phase. * Molality * Molality is the concentration of a solution expressed in moles of solute per kilogram of solvent. * molality (m) =

* What is the concentration, in molality, of a solution made by dissolving 0.500 moles of ammonia (NH3) in 1.8 kilograms of water? * molality (m) =

* molality (m) =

* molality (m) = 0.28 m

* Ionic Solutes and Electrolytes * When an ionic compound dissolves, the ionic bonds are broken and the positive and negative ions separate from each other as they are surrounded by solvent particles. * Ionic solutes are categorized as electrolytes, solutes that dissolve in water to form solutions that are able to conduct an electrical current. Pure water does not conduct electricity well; it is the ions present in tap water and lake water that make it able to conduct electricity. Because ionic solutes break apart into individual ions when they dissolve, the number of total moles of solute is determined by the total moles of ions and not the moles of ionic formula units. * Change in Boiling Point * The boiling-point elevation of a solution is directly related to the concentration of the solution measured in the unit molality (m). This means that the more solute dissolved in a solution, the higher the resulting boiling point of that solution. * Δtb = Kbm * The triangle in this equation is the Greek letter delta, which is used by chemists to represent change, while the letter t represents temperature. Together, Δtb represents the boiling point elevation, or the increase in the boiling point of a solvent caused by the given amount of solute. The unit for the boiling-point elevation is degrees Celsius (°C). This change can be added to the normal boiling point of the pure solvent to determine the new boiling point of the solution. * This equation uses a constant, Kb, known as the molal boiling point constant. This constant is dependent on the identity of the solvent, but its unit is always expressed in degrees Celsius over molality (°C/m). * Change in Freezing Point * Δtf = Kfm * Δtf represents the freezing point depression, or the decrease in the freezing point of a solvent caused by the given amount of solute. The unit for the freezing-point depression is degrees Celsius (°C). The value of this change in temperature will always be negative because the freezing point of a solution is always lower than the freezing point of the pure solvent. * The molal freezing point constant of water is -1.86 °C/m * Determining the Molar Mass of a Solute * The solution is cooled or heated to observe the freezing-point depression or boiling-point elevation. This data can then be used to determine the molar mass of the solute. * Δtb/f = Kb/f

* molar mass of solute (g/mol) =