To calculate the energy change when 85.3 grams of chlorine ([tex]\(Cl_2\)[/tex]) reacts in the given reaction, we must follow these steps:
1. Determine the molar mass of [tex]\(Cl_2\)[/tex]:
The molar mass of chlorine ([tex]\(Cl\)[/tex]) is approximately 35.453 grams per mole. Since [tex]\(Cl_2\)[/tex] has two chlorine atoms, the molar mass of [tex]\(Cl_2\)[/tex] is:
[tex]\[
\text{Molar mass of } Cl_2 = 2 \times 35.453 = 70.906 \text{ grams per mole}
\][/tex]
2. Calculate the moles of [tex]\(Cl_2\)[/tex] in 85.3 grams:
Using the molar mass, the number of moles [tex]\((n)\)[/tex] of [tex]\(Cl_2\)[/tex] can be determined using the formula:
[tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
n = \frac{85.3}{70.906} \approx 1.203 \text{ moles}
\][/tex]
3. Calculate the energy change using the given [tex]\(\Delta H\)[/tex]:
The enthalpy change ([tex]\(\Delta H\)[/tex]) for the reaction involving 3 moles of [tex]\(Cl_2\)[/tex] is 464 kJ. Therefore, for 1 mole of [tex]\(Cl_2\)[/tex], the enthalpy change is:
[tex]\[
\Delta H = 464 \text{ kJ/mol}
\][/tex]
The total energy change for 1.203 moles of [tex]\(Cl_2\)[/tex] is:
[tex]\[
\text{Energy change} = 1.203 \times 464 \approx 558.193 \text{ kJ}
\][/tex]
4. Express the energy change to three significant figures:
The energy change to three significant figures is:
[tex]\[
558 \text{ kJ}
\][/tex]
Thus, the energy change [tex]\(\Delta H\)[/tex] when 85.3 grams of chlorine reacts in the given reaction is:
[tex]\[
\boxed{558} \text{ kJ}
\][/tex]
