Question

1. a chemist wants to determine empirically the enthalpy change for the reaction: mg(s) + 2hcl(aq) → mgcl₂(aq) + h₂(g). the chemist uses a coffee - cup calorimeter to react 0.50g mg ribbon with 100ml of 1.00mol/l hcl. the initial temperature of the hcl is 20.4°c. after neutralization, the highest recorded temperature is 40.7°c. calculate the enthalpy change, in kj/mol of mg for the reaction (-4.1×10²kj/mol)

Explanation:

Step1: Calculate mass of solution

Assume density of solution = 1 g/mL, so mass $m = 100\,\text{mL} \times 1\,\text{g/mL} = 100\,\text{g}$

Step2: Calculate heat absorbed by solution

Use $q = mc\Delta T$, $c = 4.18\,\text{J/g·°C}$, $\Delta T = 40.7 - 20.4 = 20.3\,\text{°C}$
$q = 100 \times 4.18 \times 20.3 = 8485.4\,\text{J} = 8.4854\,\text{kJ}$

Step3: Calculate moles of Mg

Molar mass of Mg = 24.305 g/mol, moles $n = \frac{0.50}{24.305} \approx 0.02057\,\text{mol}$

Step4: Calculate enthalpy change

Reaction releases heat, so $\Delta H = -\frac{q}{n} = -\frac{8.4854}{0.02057} \approx -412\,\text{kJ/mol} \approx -4.1 \times 10^2\,\text{kJ/mol}$

Answer:

$-4.1\times10^2\,\text{kJ/mol}$