To solve this we are going to use the ideal gas law formula, PV=nRT, where R=0.08206L-atm/mol-K, n is the number of moles of gas, P is the pressure in atm,, T is the temperature in Kelvin and V is the volume in liter. This applies to the hydrogen gas.
PV=nRT ---> n= PV/RT
Let the mass of zinc be m and the molecular weight of zinc be M.
The above reaction implies that the number of moles of Zinc is equal to the number of moles of Hydrogen has. This can be translated as follows:
Number of moles of zinc=(PV/RT). Given that the number of moles=m/M, we get:
(m/M)= (PV/RT)--->m= M x (PV/RT).
We need to convert the temperature to Kelvin. T= 25 degrees C +273= 298K
Upon plugging in the numbers, we get: m= 65.38 g/mol x (1atm x 10.0/0.08206L-atm/mol-K x298K)= 26.7g
Thus, we have shown that 26.7 grams of zinc are required to produce 10.0L of hydrogen gas under the given conditions.