This question is asking us to find the number of moles of NaCl that we would need to produce 8.0L of Cl2 gas at STP, and it gives us the balanced chemical equation that describes the reaction.
2NaCl + 2H2O ----> 2NaOH + Cl2
From looking at the information in the question, we can see that we are given a value for volume which we can call V. We also were told that the container that the gas was in was at STP, or Standard Temperature and Pressure which always means that the gas is at 0°C, or 273.15K and 1 atmosphere (atm) of pressure.
Knowing this, we can make a list of everything we have and see where to go from that
P = 1atm
V = 8L
moles (n) = ?
T = 273K
With all of these values and and the fact that we are dealing with Cl2 gas, we can use the ideal gas law, PV=nRT to solve for the amount of Cl2 gas that was generated. We should also note that since we are using the units L, atm, mol, we will use the gas constant R = 0.08206
PV=nRT
PV = n
RT
1atm X 8L = n
0.08206((L*atm)/(mol*K)) X 273K
n = 0.3571 mol Cl2 gas
From this, we can use the chemical equation to find the number of moles of NaCl needed to create this gas. In the equation
2NaCl + 2H2O ----> 2NaOH + Cl2
we can see that for every one mole of Cl2, there are 2 moles of NaCl. There are twice as many moles. Therefore, all we have to do is multiply the number of moles by two to get the answer!
0.3571 mol Cl2 X ((2 mol NaCl)/(1 mol Cl2)) = 0.7142 mol NaCl
Finally, to correct for significant figures, we are left with 0.71 moles of NaCl needed to create 8.0L of Cl2 gas