Question

For each problem below, write the equation and show your work. 1. a. What is the molar heat capacity of liquid water? (note: the molar heat capacity is the heat required to raise 1 mole by 1 degree Celsius in J/mol⋅°C rather than J/g°C) b. What is the heat capacity of 6.50 mol of liquid water? c. How many kJ of heat are needed to raise the temperature of 38.5 mol of water from 38.1°C to 79.4°C? 2. The specific heat of toluene, C₇H₈, is 1.13 J/gK. How many joules of heat are needed to raise the temperature of 40.0 g of toluene from 10.4^∘ C to 28.0°C ? 3. When a 4.25 g sample of solid ammonium nitrate dissolves in 60.0 g of water in a coffee-cup calorimeter, the temperature drops from 22.0°C to 16.9°C. Calculate ΔH( in kJ/molNH₄NO₃ ) for the solution process NH₄NO₃ ( s)→NH₄⁺(aq)+NO₃ (aq) Assume that the specific heat of the solution is the same as that of pure water. 4. A 1.800 g sample of octane, C₉H₁₈ was burned in a bomb calorimeter whose total heat capacity is 11.66 kJ°C. The temperature of the calorimeter plus contents increased from 21.36°C to 28.78°C. What is the heat of combustion per gram of octane? per mole of octane?

Answer 1

a. The molar heat capacity of liquid water (Cp) is approximately 75.3 J/mol⋅°C.

b. To find the heat capacity (Q) of 6.50 mol of liquid water, we can use the equation:

Q = Cp * ΔT * n

where ΔT is the change in temperature and n is the number of moles.

Assuming a constant heat capacity, we have:

Q = 75.3 J/mol⋅°C * ΔT * 6.50 mol

c. To calculate the heat (Q) needed to raise the temperature of 38.5 mol of water from 38.1°C to 79.4°C, we use the equation:

Q = Cp * ΔT * n

where ΔT is the change in temperature and n is the number of moles.

Assuming a constant heat capacity, we have:

Q = 75.3 J/mol⋅°C * (79.4°C - 38.1°C) * 38.5 mol

The heat (Q) required to raise the temperature of a substance can be calculated using the formula:

Q = m * Cp * ΔT

where m is the mass, Cp is the specific heat capacity, and ΔT is the change in temperature.

Given that the specific heat of toluene is 1.13 J/gK, the mass is 40.0 g, and the temperature change is (28.0°C - 10.4°C), we can substitute the values into the formula to calculate Q.

To calculate the enthalpy change (ΔH) for the solution process of solid ammonium nitrate (NH₄NO₃) dissolving in water, we can use the equation:

ΔH = Q / n

where Q is the heat absorbed or released and n is the number of moles of ammonium nitrate.

Given the mass of the ammonium nitrate sample (4.25 g), the temperature change (22.0°C - 16.9°C), and the mass of water (60.0 g), we can calculate Q. Then, by dividing Q by the number of moles of ammonium nitrate, we can find ΔH.

Assuming the specific heat of the solution is the same as that of pure water, we can use the equation:

Q = m * Cp * ΔT

The heat of combustion per gram of octane can be calculated using the formula:

ΔH = Q / m

where Q is the heat released in the combustion reaction and m is the mass of octane.

Given the mass of the octane sample (1.800 g) and the temperature change (28.78°C - 21.36°C), we can calculate Q. Then, by dividing Q by the mass of octane, we can find the heat of combustion per gram of octane.

To find the heat of combustion per mole of octane, we need to convert the mass of octane to moles using the molar mass of octane (C₉H₁₈). Then, we can divide Q by the number of moles of octane.