To determine the enthalpy of the reaction when 1.00 g of solid potassium (K) is added to water and releases 4610 J of energy, follow these detailed steps:
1. Determine the Molar Mass of Potassium (K):
The molar mass of potassium (K) is approximately 39.1 grams per mole (g/mol).
2. Calculate the Number of Moles of Potassium (K):
You start with a mass of potassium of 1.00 g.
To find the number of moles of potassium, use the formula:
[tex]\[
\text{Moles of K} = \frac{\text{Mass of K}}{\text{Molar Mass of K}}
\][/tex]
Thus,
[tex]\[
\text{Moles of K} = \frac{1.00 \, \text{g}}{39.1 \, \text{g/mol}} \approx 0.0256 \, \text{mol}
\][/tex]
3. Determine the Energy Released per Mole of Potassium (K):
The given energy released is 4610 J.
To find the enthalpy of the reaction (which is the energy released per mole of K), use the formula:
[tex]\[
\Delta H = \frac{\text{Energy Released}}{\text{Moles of K}}
\][/tex]
Plug in the numbers we have:
[tex]\[
\Delta H = \frac{4610 \, \text{J}}{0.0256 \, \text{mol}} \approx 180251 \, \text{J/mol}
\][/tex]
Convert this value to kJ/mol, knowing that 1 kJ = 1000 J:
[tex]\[
\Delta H \approx 180.251 \, \text{kJ/mol}
\][/tex]
Therefore, the enthalpy of the reaction when 1.00 g of solid potassium is added to water, releasing 4610 J of energy, is approximately [tex]\(\boxed{180.251 \, \text{kJ/mol}}\)[/tex].
