Certainly! To determine the enthalpy change (ΔH) of the reaction in kJ/mol given the data, we need to follow these steps:
### Step 1: Determine the molar mass of [tex]\( KNO_3 \)[/tex].
The molar mass of [tex]\( KNO_3 \)[/tex] is calculated by adding the atomic masses of potassium (K), nitrogen (N), and three oxygen (O) atoms:
[tex]\[
K = 39.1 \text{ g/mol}, \quad N = 14.0 \text{ g/mol}, \quad O_3 = 3 \times 16.0 \text{ g/mol}
\][/tex]
[tex]\[
\text{Molar mass of } KNO_3 = 39.1 + 14.0 + 48.0 = 101.1 \text{ g/mol}
\][/tex]
### Step 2: Convert the mass of [tex]\( KNO_3 \)[/tex] to moles.
Given mass of [tex]\( KNO_3 \)[/tex] is 7.5 g. To find the number of moles, we divide the mass by the molar mass:
[tex]\[
\text{Moles of } KNO_3 = \frac{7.5 \text{ g}}{101.1 \text{ g/mol}} = 0.074184 \text{ moles}
\][/tex]
### Step 3: Convert the energy absorbed from Joules to kJ.
The energy absorbed by the reaction is given as 2597 J. Since 1 kJ = 1000 J, we convert Joules to kilojoules:
[tex]\[
\text{Energy absorbed} = \frac{2597 \text{ J}}{1000 \text{ J/kJ}} = 2.597 \text{ kJ}
\][/tex]
### Step 4: Calculate the enthalpy change (ΔH) per mole of [tex]\( KNO_3 \)[/tex].
ΔH is the energy change per mole of substance. We divide the energy absorbed in kJ by the number of moles of [tex]\( KNO_3 \)[/tex]:
[tex]\[
\Delta H = \frac{2.597 \text{ kJ}}{0.074184 \text{ moles}} = 35.008 \text{ kJ/mol}
\][/tex]
Since the reaction absorbs energy, ΔH will be positive:
[tex]\[
\Delta H = + 35.01 \text{ kJ/mol (to four significant figures)}
\][/tex]
Therefore, the enthalpy change (ΔH) for the given reaction is [tex]\( +35.01 \, \text{kJ/mol} \)[/tex].
