Lec 21: Quantifying Heat Flow and Calorimetery

How much heat must a 15.0 g sample of water absorb to raise its temperature from 25 °C to 55 °C? (Specific heat capacity of water is 4.18 J·g-1·°C-1)

(15)(4.18)(55-25) = q q = 1881 J q = 1.88 kJ

If an object has a specific heat of 0.981 Jg∘C, absorbs 674 J of heat, and experiences a 12.0∘C temperature increase, what is the object's mass in grams?

+674 = m(0.981)(12.0∘C) m = 57.25g

Equation for heat energy transfer

+q = -q +(mC∆T) = -(mC∆T)

A piece of iron with a mass of 72.4 g is heated to 100.0 °C and plunged into 100.0 g of water that is initially at 10.0 °C. Calculate the final temperature that is reached, assuming no heat loss to the surroundings (specific heat capacity of Fe(s) = 0.449 J/g·°C and specific heat capacity of H2O(l) = 4.18 J/g·°C).

-q Fe = + q H2O q=mC∆T -q Fe: -[(72.4)(0.449)(Tf-100)] = -32.5Tf + 3250 q H2O: (100)(4.18)(Tf-10) = 418Tf - 4180 -32.5Tf + 3250 = 418Tf - 4180 451Tf = 7430 Tf = 16.5°C The entire system has a final temp of 16.5°C

The SI unit for energy is the Joule. Which of the following is/are equal to 1 Joule?

1N×m 1kg×m2/s2

Graphite has a specific heat capacity of 0.709 J/g ∘C. Determine the change in energy in joules if a 25.0 g sample of graphite has a temperature change of −17.0 ∘C.

C = 0.709 J/g ∘C m = 25.0 g ∆t = −17.0 ∘C q = ? mC∆T = -301.325J The answer is negative because q represents the amount of heat flowing into the system. For the system to cool, heat must flow out, and q -- and in this case ΔE -- are negative.

C = Q/T

C = heat absorbed/ change in temp C + q +/- ∆t +/-

Calculate the heat capacity of 1,343 g of lead, given that 45 J is needed to raise the temperature by 29.8 ∘C.

Heat capacity (C) is the ratio of q and ∆t C = 45J / 29.8C C = 1.51 J/C

How do you determine which q is - and +?

If you have a metal ball of Fe that is 100°C and water that is H2O that is 25°C, the metal will be -q (losing heat) and the water will be +q (gaining heat)

Unit for heat capacity

J/°C

Manganese reacts with hydrochloric acid to produce manganese(II) chloride and hydrogen gas. Mn(s) + 2HCl(aq) → MnCl2(aq) + H2(g) When 0.625 g Mn is combined with enough hydrochloric acid to make 100.0 mL of aqueous solution in a coffee cup calorimeter, all of the Mn reacts, raising the temperature of the solution from 23.5 °C to 28.8 °C. Find ΔHrxn for the reaction in kJ·mol-1 of Mn. (Assume that the specific heat capacity of the solution is 4.18 J·g-1·°C-1 and that the density of the solution is 1.00 g·mL-1)

Mn m = 0.625 g Mn solution: v = 100.0 mL d = 1.00 g·mL-1 C = 4.18 J·g-1·°C-1 ∆t = 28.8-23.5 = 5.3C Find ΔHrxn for the reaction in kJ·mol-1 of Mn. Find q = mC∆T mass = V(D) q = (100mL)(1.00 g·mL-1)(4.18 J·g-1·°C-1)(5.3C) q = 2215.4 J What is heat flow for Mn? -q = -2215.4 J J → kJ -2.2154 kJ g → mol Mn 0.625g/ 54.938044 g/mols =0.01137mol -2.2154 kJ / 0.01137mol = -194.85 kJ/mol

Is specific heat capacity dependent on mass?

No; only total heat capacity is

A 1.00 g sample of hydrazine (N2H4) is burned in a bomb calorimeter containing 1200 g of water that experiences a temperature change of 3.54∘C. If the heat capacity of the calorimeter is 840 J C, what is the heat of combustion for 1 mole of the sample?

Solve for the q rxn by adding q water and q calorimeter and making it neg. Then convert grams to mols for N2H4 and divide the q rxn by the number of mols

One cast iron pan has a mass of 2.26kg and a second cast iron pan has a mass of 3.54kg. Both cast iron pans have the same alloy composition. Which of the following statements are true? (select all that apply)

Specific heat capacity (J/g°C) Heat Capacity (J/°C) 1. The two pans will have the same specific heat capacity. 2. The heat capacity of the larger pan will be greater than the heat capacity of the smaller pan. The specific heat capacities for the two pans are the same because they are made of the same material. The same material will have the same properties when mass is not involved. The heat capacity is equal to the mass times the specific heat capacity; therefore, the more massive pan will have a larger heat capacity than the less massive pan.

Calorimetry

The precise measurement of heat flow out of a system for chemical and physical processes

The specific heat capacities of gold and copper are 0.129 J·g-1·°C-1 and 0.387 J·g-1·°C-1, respectively. At 25 °C, 230 J of heat is added to 10.0 g samples of pure gold and copper. select the correct statement about temperature change. (Note: You can answer this question without detailed calculations.)

The temperature of the gold sample will rise higher than that of the copper sample; has a lower heat capacity

Which unit of energy is defined as the amount of energy required to raise the temperature of one gram of water by 1∘C?

calorie

Is heat capacity extensive or intensive?

extensive, depends on the amount of substance. It is not helpful to compare to other substances because it is dependent on the amount of substance. In order to compare, you need to divide it by an intensive property to turn it from extensive to intensive. To turn heat capacity (C) with unit J/°C, into an intensive property, we divide it by mass. It becomes J/g*°C

Endothermic reaction

heat "gained" by the reaction is "lost" by the water q sol = -qrxn

Heat Energy Transfer

heat energy flows from the hotter substance to the cooler substance until they reach a common final temperature.

Exothermic reaction

heat lost by reaction is gained by the water, so the temp rises -q rxn = q sol

The specific heat of air is 1.007J/g°C and the specific heat of nitrogen (N2) is 1.040J/g°C. What is the specific heat of oxygen (O2)?

less than 1.007J/g°C ; Air contains mostly nitrogen and oxygen. Since the specific heat of nitrogen is larger than the specific heat of air, the specific heat of oxygen must be smaller than the specific heat of air.

Calculate the specific heat capacity of aluminum if a 16.0 g sample of aluminum has a temperature change of 36.2 °C when it gained 522 J of heat energy.

m = 16.0g t = 36.2°C q = +522 J C = ? 522/ (36.2 * 16) = 0.901J/g°C

The specific heat capacity of aluminum is 0.903 J·g-1·°C-1. Calculate the quantity of heat required to raise the temperature of a 5.00 g sample of aluminum from 25.2 °C to 55.1 °C.

m = 5.00g t₁ = 25.2°C t₂ = 55.1 °C q = ? C = 0.903 J·g-1·°C-1 ∆t = 55.1 - 25.2 = 29.9 °C q = 0.903(29.9)(5.00) q = 135 J

Methane gas burns in air to form carbon dioxide and water, releasing heat. CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) ΔHrxn = -802.3 kJ What minimum mass of CH4 is required to heat 55.0 g of water by 25.0 °C? (Assume that no heat is lost to the environment; specific heat capacity of water is 4.18 J·g-1·°C-1).

mC∆T Methane: m = ? Water: m = 55.0 g C = 4.18J/gC ∆T = 25.0 C (55

When 0.243 g of Mg metal is combined with enough HCl to make 100. mL of solution in a coffee cup calorimeter, the following reaction occurs. Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) If the temperature of the solution increases from 23.0 to 34.1 °C as a result of the reaction, calculate DHrxn in kJ·mol-1 of Mg. Assume that the solution has a specific heat capacity of 4.18 J/g·°C and a density of 1.00 g·mL-1

mC∆T Since you are not given the heat capacity for Mg and you know that heat calorimetry is the same flow of energy as it is how, we can measure the heat flow of the water instead. Then, we simply add the correct sign (+/-) to demonstrate if heat is moving in or out of the system. C: 4.18J/gC m: 100 mL (1.00g/mL) = 100. g ∆t: 34.1-23.0 = 11.1C Since the temperature of the solution increased, that means that the reaction is releasing heat and water is GAINING (+q) +q = (100g)(4.18)(11.1) = 4.64 x 10^3 J Since -q = +q, we just change the sign to find the ∆H rxn -q = -4.64x10^3J They ask you to find the ∆Hrxn in kJ/mol for Mg Moles 0.243g / 24.31 = 0.00999 mol Hg Convert J to kJ -4.64 x 10^3 J / 10^3 = -4.64 kJ -4.64 kJ / 0.00999 mol Hg = 464.46 kJ/mol Mg

coffee cup calorimeter

piece of equipment designed to measure for reactions at constant pressure; used to find change in enthalpy for substances that are dissolved in water

2.25 g of C6H12O6 is burned in a bomb calorimeter containing 550. g of water and the temperature increases from 25.0∘C to 38.6∘C. If the bomb has a heat capacity of 893 J/∘C, what is the value for q of the reaction?

q rxn = -[qwater + qbomb] q water = 4.184(550)(13.6) = 31,296 J qbomb = (893 J/∘C)(13.6∘C) = 12145J q rxn = -(31,296 J+12,145 J) **negative because the reaction is releasing heat, that is why there is an increase temperature in the water and bomb (external) =−43,441 J or −43,400 J with three significant figures.

A 0.500 g sample of C7H5N2O6 is burned in a calorimeter containing 600. g of water at 20.0∘C. If the heat capacity of the bomb calorimeter is 420.J∘C and the heat of combustion at constant volume of the sample is −3374kJmol, calculate the final temperature of the reaction in Celsius. The specific heat capacity of water is 4.184 Jg ∘C.

q water: (600)(4.1840(F-20) q calorimeter: (420)(F-20) Find the q rxn in J instead of kJ/mol moles: = 0.500g / 213.124 = 0.2346 mol C7H5N2O6 (−3374kJ/mol) 0.2346 mol = -7.92 kJ (-7.92kJ)(10^3) = -7915.58J -7915.58J = -[(600)(4.1840(F-20) + (420)(F-20)] F = 22.7°C

5.0 g of C8H18 are burned in a bomb calorimeter with 750 g water, and there is 10.0∘C increase in temperature when 32.0 kJ of heat is released. What is the heat capacity of the calorimeter?

qrxn = −[qwater+qbomb] q rxn: -32.0 kJ → -32000J q water: (750)(4.184)(10) = 31380 J -32000J = -31380 J - (C calormeter)(10) C cal = 62 J/°C

2.50 g C8H18 is burned in a bomb calorimeter with a heat capacity of 837 J∘C and containing 745 g of water, and the temperature goes from 15.0∘C to 33.8∘C. How much heat, in kilojoules, is released by the reaction? The heat capacity of water is 4.184 Jg ∘C

qrxn = qwater + qbomb qwater: = 4.184(745)(13.6)(18.8) = 42392.288 J q bomb: (893 J/∘C)(18.8∘C) = 16788.4 J ** the reaction releases heat which makes the q of the rxn neg q rxn: = -(42392.288 J + 16788.4 J) = -74336.704 = -74.34 kJ Finally, since q represents the flow of heat into the system, a negative value of q means heat is lost from the system. Therefore, 74.3kJ of heat are released.

6.45 g of C6H12O6 is burned in a bomb calorimeter containing 950. g of water and the temperature goes from 35.0∘C to 42.3∘C. If the bomb has a heat capacity of 933 J∘C, what is the value for q of the reaction?

qrxn = qwater + qbomb qwater: = 4.184(950)(7.3) = 29016.04 J q bomb: (933 J/∘C)(7.3∘C) = 6810.9 J q rxn: 29016.04 J + 6810.9 J = -35826.94 J

heat capacity

the number of heat units needed to raise the temperature of a body by one degree.