Question

A 1.00 x 102mL sample of 0.200 M aqueous hydrochloric acid is added to 1.00 x 102mL of 0.200 M aqueous ammonia in a constant-pressure calorimeter of negligible heat capacity. The following reaction occurs when the two solutionsare mixedHCl(aq)+ NH3(aq)--->NH4Cl(aq)The temperature increase is 2.34°C. Calculate heat change of the reaction per mole of HCl reacted.Assume that the densities and specific heats of the solutions are the same as for water (1.00 g/mL and 4.184 J/g · °C, respectively)

Answer 1

ΔH = -98 kJ/mol

Step-by-step explanation:

To calculate the heat change of the reaction:

HCl(aq) + NH₃(aq) → NH₄Cl(aq)

0.2M 0.2M ΔT=2.34°C

1x10²mL 1x10²mL

We need to use the next equation:

`q = mc \Delta T` (1)

where q: the amount of heat energy lost or gained, m: the mass of the substance, c: the specific heat capacity of the substance and ΔT: the change in temperature of the substance

Assuming that the densities of the solutions are the same as for water, we can determine the mass of the solution:

`d = \frac {m}{V}`

where d: density, m: mass and V: volume of solution = 100 + 100 = 200mL

`m = d \cdot V = 1 \frac {g}{mL} \cdot 200mL = 200g`

Now, using the calculated mass in equation (1), and assuming that the specific heats of the solutions are the same as for water, we can find heat change of the reaction:

`q = 200g \cdot 4.184 \frac {J}{g \cdot ^(\circ)C} \cdot 2.34^(\circ)C`

`q = 1.96 \cdot 10^(3)J`

This heat is negative because is the heat lost by the reacting HCl and NH₃ and gained by the water, so:

`q = - 1.96 \cdot 10^(3)J`

To calculate the heat change of the reaction per mole of HCl, we need to divide the heat change by the number of moles, which is called the enthalpy of reaction:

`\Delta H = \frac {q}{moles}`

`\Delta H = \frac {q}{moles}`

`\Delta H = \frac {-1.96 \cdot 10^(3) J}{0.2 (mol)/(L) \cdot 0.1L}`

`\Delta H = -98 \cdot 10^(3) (J)/(mol) = -98 \frac {kJ}{mol}`

So, the heat change of the reaction per mole of HCl reacted, often called enthalpy of reaction, is ΔH = -98 kJ/mol.

Have a nice day!