Thermodynamics chemical reaction problem

[Benzoate]

Homework Statement

What are q and w (in kJ) for the reaction of 22 g of Na(s) and 82 g of Cl2(g) to produce NaCl at 1 atm and 298 K.

Homework Equations

w=-delta(n(g))* R*T where delta(n(g)) = the moles of gas created during the reaction

The Attempt at a Solution

First, I wrote the chemical reaction for Na and Cl2

2Na(s) +Cl2(g)=> 2NaCl

delta(n(g))=0-1 = -1

82 g Cl2*(1 mol Cl2/70.98 g Cl2)*(-1 mol gas/1mol Cl2)= -1.16

delta n(g) =-1.16
w=-delta(n(g))*RT=(-1.16)(8.314)(298 K)=2.87 kJ

But that's not the answer according to the back of my textbook.

 

[Astronuc]

The volume is changing from the volume of Cl₂ gas to essentially zero.

Can one apply w = p $\Delta{V}$? 1 mole of gas has a volume of 22.4 l.

Then there is the heat.