Water and the Changes of State The energy required to heat (or cool) a solid (or heat/cool a liquid or a gas) can be calculated using q = ms  T. It requires additional energy to change states. The energy required to convert a specific amount of the solid to a liquid is known as the heat of fusion (q =  H fus ) and the energy required to convert a specific amount of a liquid to a gas is the heat of vaporization (q =  H vap ). The total amount of energy can be calculated from q T = q 1 + q 2 + q 3... Temperature o C Heating curve for water

Water and the Changes of State Q. How many kilojoules of energy are needed to change 15.0 g of ice at o C to steam at o C? The first step is to design a pathway: q 1 = ms  T for ice from -5.0 to 0.0 o C, the specific heat of ice is J/g o C q 2 =  H fus for ice to liquid at 0.0 o C q 3 = ms  T for liquid 0.0 o C to o C q 4 =  H vap for liquid to steam at o C q 5 = ms  T for steam to o C; the specific heat of steam is J/g o C so q T = q 1 + q 2 + q 3 + q 4 + q 5 The next step is to calculate each q: q 1 = (15.0 g) (4.213 J/g o C) (0.0 - (-5.0) o C) = 316 J q 2 = (335 J / g) (15.0 g) = 5025 J q 3 = (15.0 g) (4.184 J/g o C) ( (0.0) o C) = 6276 J q 4 = (2260 J / g) (15.0 g) = J q 5 = (15.0 g) (1.900 J/g o C) ( o C) = 285 J q T = 316 J J J J J = 45.8 kJ

Energy & Change of State SI unit of energy = Joule (J) The energy required to vaporize a substance, q, is proportional to the amount of substance. This energy is called the heat of vaporization,  H vap. The process is endothermic, therefore  H vap is positive.  H vap = q/m → q =  H vap x m When vapor condenses into a liquid, the reverse energy change, heat energy is removed from the substance. Known as the heat of condensation. This process is exothermic, therefore  H con is negative.

To melt a solid, energy must be added to overcome the forces that hold the crystal structure together. This is known as the heat of fusion,  H fus. The process is endothermic, therefore  H fus is positive.  H fus = q/m → q =  H fus x m  H fus of a substance is the energy required to melt one gram of that substance. The heat of solidification is the reverse of heat of fusion and is exothermic and  H sol is negative. Energy & Change of State

Energy & Change of Temperature: Specific Heat The specific heat is the heat flow required to change the temperature of one gram of a substance by one degree Celsius, c. q = m x c x  T Specific heat of water = 4.18 J/g °C = 1 cal/g °C 1 cal = J

Change in Temperature plus Change of State If you were to take some ice from a freezer, place it in a flask and apply steady heat to it, five things would happen: The ice would warm to its melting point. The ice would melt at the melting point. The water would warm to its boiling point. The water would boil at the boiling point. The steam would become hotter.

How to calculate the total heat flow for a change in temperature plus a change of state Step 1 : Sketch a graph having the shape shown on the next slide. Be sure to mark all relevant starting and ending points. Step 2: Calculate the heat flow, q, for each parts of the graph between all of the starting and ending points. Step 3: Add the heat flows. Be sure the units are the same, either kilojoules or joules, for all numbers being added.

Sample problem for a change in temperature plus a change of state Problem: Calculate the total heat flow when 19.6 grams of ice, initially at -12°C, is heated to steam at 115°C. Required information: Given: m = 19.6 g T i = -12°C T f = 115°C Look up the following: T m = 0°CT b = 100ºC  H fus = 335 J/g  H vap = 2.26 kJ/g

Answer: q 1 = 0.48 kJ q 2 = 6.53 kJ q 3 = 8.19 kJ q 4 = 44.3 kJ q 5 = 0.59 kJ  q = q 1 + q 2 = q 3 + q 4 + q 5 = 60.1 kJ Set up for answers q1 = m x c x  T q2 = m x  H fus q3 = m x c x  T q4 = m x  H vap q5 = m x c x  T

PRACTICE PROBLEMS #21a 1. Which contains less heat, ice at 0 o C or water at 0 o C? Explain your answer. 2. On the basis of KMT, explain why vapor pressure increases with temperature. 3. Write equations to show how the following metals react with water. a) aluminumb) calcium c) potassium d) iron Ice at 0 o C contains less heat than liquid water at the same temperature. Heat must be added to convert ice to water, so the water will contain that much more additional heat energy. Also the liquid state is in motion much more than the solid state. An increase in motion can only be accomplished by an increase in energy. According to the kinetic molecular theory, the vapor pressure of a liquid should increase with temperature because of the increase in collisions and kinetic energy that always accompanies an increase in heat energy (temperature). KE m = 3 / 2 RT. The increase in energy thus motion allows the liquid molecules to escape (overcome the surface tension and other cohesive forces maintaining the liquid state) from the surface of the liquid into the gas phase. a) Al (s) + 3H 2 O (g)  3H 2 (g) + Al 2 O 3 *requires steam b) Ca (s) + 2H 2 O  H 2 (g) + Ca(OH) 2 *slowly at ambient temperature c) 2K (s) + 2H 2 O  H 2 (g) + 2KOH + heat * vigorous at ambient temperature d) 3Fe (s) + 4H 2 O (g)  4H 2 (g) + Fe 3 O 4 *requires steam

PRACTICE PROBLEMS #21b 1. Explain the physical process of boiling. 2. Why does ice float in water? 3. Why does water have a relatively high boiling point? 4. Explain if ice will float in ethyl alcohol (d = g/L)? 5. How much energy is needed to change g of water at o C to steam at o C? 6. Magnesium carbonate, MgCO 3, forms a hydrate containing 39.1 % water of hydration. Calculate the formula of this hydrate. See next slide for essay/answer x 10 5 J or x 10 4 cal MgCO 3. 3 H 2 O

1. Explain the physical process of boiling. At room temperature the water molecules have enough energy to allow the particles to move past each other but not enough to escape the surface tension. As the temperature of water increases, the heat energy (from the burner) is transferred to kinetic energy (for the molecules) leading to an increase in the molecular motion of the molecules. This action results in an increase in the vapor pressure above the surface of the liquid. When the vapor pressure of the water equals the external pressure, boiling begins. Now a sufficient amount of the molecules have enough energy to resist the attractive forces. Bubbles of vapor are formed throughout the liquid and these bubbles rise to the surface to escape.

2. Why does ice float in water? Ice floats in its own liquid due to the intermolecular force, hydrogen bonding. As water freezes, the molecular motion of the molecules slow down and the partial positive end (hydrogen) of one water molecule is attracted to the partial negative end (oxygen) of another water molecule. Combine this event with the bent shape of water and the molecules become arranged in a 3-D hexagonal array. This array creates pockets of vacuum (empty space) in the lattice structure as well as a decrease in the number of molecules per unit volume. The mass is directly related to the number of molecules therefore, in the solid state, since there are less particles then there must be less mass per unit volume therefore the solid is less dense than the liquid.

3. Why does water have a relatively high boiling point? Water has a relatively high boiling point because of the amount of intermolecular forces present. Water experiences LDF (London Dispersion Forces) and d-d (dipole-dipole) forces, along with the additional attractive force, Hydrogen bonding. A large amount of heat energy is required to break all of these forces in order for a phase transition to occur, thus the high boiling point. 4. Explain if ice will float in ethyl alcohol (d = g/L)? Ice would not float in pure ethyl alcohol because the density of water is g/mL which is greater than g/mL for ethyl alcohol. Yet since ethyl alcohol also undergoes a small degree of hydrogen bonding, the sinking effect is not as dramatic as it would be with a nonpolar substance.

GROUP STUDY PROBLEMS #21 Short Essay 1. Can ice be colder than 0.0 o C? Justify your answer. 2. Why does a boiling liquid maintain a constant temperature when heat is continually being added? 3. Why does a lake freeze from the top down? Math 1. Suppose 50.0 g of ice at 0.0 o C are added to 285g of water at 22.0 o C. Is there sufficient ice to lower the temperature of the system to 0.0 o c and still have ice remaining? Show all work. 2. A mixture of 70.0 mL of hydrogen and 50.0 mL of oxygen is ignited to form water. Does any gas remain unreacted? 3. A 25.0 g sample of a hydrate of FePO 4 was heated until all the water was driven off. The mass of anhydrous sample is 16.9 g. What is the formula of the hydrate?