To determine the enthalpy of the reaction (ΔH_rxn), we need to follow a series of steps involving conversions and calculations. Here's a detailed step-by-step solution:
1. Know the Given Values:
- Energy released, \( Q \) = 4610 Joules (J)
- Mass of potassium, \( m \) = 1.00 grams (g)
- Molar mass of potassium, \( M_{\mathrm{K}} \) = 39.10 g/mol
2. Calculate the Number of Moles of Potassium:
The number of moles of potassium, \( n \), can be calculated using the formula:
[tex]\[
n = \frac{m}{M_{\mathrm{K}}}
\][/tex]
Substituting the given values:
[tex]\[
n = \frac{1.00 \, \text{g}}{39.10 \, \text{g/mol}} \approx 0.02557544757033248 \, \text{mol}
\][/tex]
3. Convert the Energy Released to Kilojoules:
Since enthalpy (ΔH_rxn) is usually given in kilojoules per mole, we need to convert the energy from joules to kilojoules:
[tex]\[
Q_{\mathrm{kJ}} = \frac{Q}{1000} = \frac{4610 \, \text{J}}{1000} = 4.610 \, \text{kJ}
\][/tex]
4. Calculate the Enthalpy Change per Mole (ΔH_rxn):
The enthalpy change of the reaction (ΔH_rxn) can be calculated using the formula:
[tex]\[
\Delta H_{\mathrm{rxn}} = \frac{Q_{\mathrm{kJ}}}{n}
\][/tex]
Substituting the values we have:
[tex]\[
\Delta H_{\mathrm{rxn}} = \frac{4.610 \, \text{kJ}}{0.02557544757033248 \, \text{mol}} \approx 180.251 \, \text{kJ/mol}
\][/tex]
Therefore, the enthalpy of the reaction, [tex]\( \Delta H_{\mathrm{rxn}} \)[/tex], is approximately 180.251 kJ/mol.
