Reactivity 1.1—Measuring enthalpy changes: Practice Questions

In solution calorimetry, the heat absorbed or released by a reaction is often calculated using the formula \( q = mc\Delta T \). What quantity does \( c \) typically represent in this calculation?

In an experiment, 2.00 g of sodium hydroxide, \( NaOH \) (M = 40.00 g mol^-1), is dissolved in 100.0 cm³ of water. The temperature rises by 5.00 °C. What is the enthalpy of solution for \( NaOH \) in kJ mol^-1? (Assume the density of the solution is 1.00 g cm^-3 and the specific heat capacity of the solution is 4.18 J g^-1 K^-1).

A \(4.00 \text{ g}\) sample of \(NaOH(s)\) (molar mass \(= 40.00 \text{ g mol}^{-1}\)) is dissolved in \(100.0 \text{ g}\) of water in a calorimeter. The temperature of the water increases from \(20.0^{\circ}\text{C}\) to \(30.0^{\circ}\text{C}\). The heat capacity of the calorimeter itself is \(20.0 \text{ J K}^{-1}\). What is the enthalpy of solution for \(NaOH\) in \(\text{kJ mol}^{-1}\)? (Specific heat capacity of water \(= 4.18 \text{ J g}^{-1} \text{ K}^{-1}\))

A student adds a 50.0 g block of iron at 100.0 °C to 50.0 g of water at 20.0 °C in an insulated container. The specific heat capacity of iron is 0.450 J g^-1 K^-1 and the specific heat capacity of water is 4.18 J g^-1 K^-1. Which statement about the final temperature of the mixture, \( T_f \), is correct?

A student uses a calorimeter to determine the enthalpy of solution of ammonium nitrate. If the student incorrectly assumes the specific heat capacity of the solution is \( 4.18 \text{ J g}^{-1} \text{K}^{-1} \) when it is actually \( 3.90 \text{ J g}^{-1} \text{K}^{-1} \), how will the calculated absolute value of the enthalpy change compare to the actual value?

Suggest why the experimental enthalpy of combustion for methanol is often significantly lower than the theoretical value found in data booklets, even when using a well-insulated calorimeter.

When \( 100.0\text{ cm}^3 \) of \( 1.00\text{ mol dm}^{-3} \text{ KOH} \) reacts with \( 100.0\text{ cm}^3 \) of \( 1.00\text{ mol dm}^{-3} \text{ HNO}_3 \), the temperature increases by \( 5.50^\circ\text{C} \). If the theoretical heat released is \( 11.4\text{ kJ} \), calculate the heat capacity of the calorimeter in \( \text{J K}^{-1} \), assuming the specific heat of the solution is \( 4.18\text{ J g}^{-1}\text{ K}^{-1} \).

A sample of \( 50.0\text{ g} \) of water is heated from \( 20.0^\circ\text{C} \) to \( 45.0^\circ\text{C} \). Calculate the heat energy absorbed, in kJ, given the specific heat capacity of water is \( 4.18\text{ J g}^{-1}\text{ K}^{-1} \).

A student reacts 25.0 cm\(^3\) of \(1.00\text{ mol dm}^{-3}\) sulfuric acid, \(H_2SO_4\), with 50.0 cm\(^3\) of \(1.00\text{ mol dm}^{-3}\) sodium hydroxide, \(NaOH\). The initial temperature of both solutions was \(21.5^{\circ}C\) and the maximum temperature reached was \(30.2^{\circ}C\).
(a) Identify the limiting reactant for this neutralization reaction.
(b) Calculate the enthalpy of neutralization per mole of water formed, assuming the density of the final solution is \(1.00\text{ g cm}^{-3}\) and its specific heat capacity is \(4.18\text{ J g}^{-1}\text{ K}^{-1}\). Give your answer in \(\text{kJ mol}^{-1}\).

An experiment was conducted to determine the enthalpy change of the displacement reaction between zinc and copper(II) sulfate:
\(Zn(s) + CuSO_4(aq) \rightarrow ZnSO_4(aq) + Cu(s)\)

A student added 1.00 g of zinc powder to 50.0 cm³ of \(0.200\text{ mol dm}^{-3}\) \(CuSO_4\) solution. The temperature was recorded every minute:

Time (min): 0, 1, 2, 3 (addition), 4, 5, 6, 7, 8
Temp (\(^{\circ}C\)): 20.0, 20.0, 20.0, -, 34.2, 33.8, 33.4, 33.0, 32.6

(a) Use the data to estimate the maximum temperature rise (\(\Delta T\)) by extrapolating the cooling curve back to the time of mixing.
(b) Calculate the enthalpy change of the reaction in \(\text{kJ mol}^{-1}\) of \(CuSO_4\).