Final answer:
To calculate the mass of sodium azide required to produce a given volume of nitrogen gas, use the ideal gas law equation and the balanced equation for the decomposition of sodium azide. Then, calculate the moles of sodium azide and use the molar mass to determine the mass.
Step-by-step explanation:
To calculate the mass of sodium azide required to produce a given volume of nitrogen gas, you need to use the molar mass of sodium azide and the gas density. First, calculate the moles of nitrogen gas using the ideal gas law equation:
n = PV / RT
where P is the pressure (convert torr to atm), V is the volume in liters (convert ft^3 to L), R is the ideal gas constant, and T is the temperature in Kelvin (convert degrees Celsius to Kelvin). Rearrange the equation to solve for moles:
n = (PV) / RT
Next, use the balanced equation to find the mole ratio between sodium azide and nitrogen gas:
2NaN3(s) ⟶ 2Na(s) + 3N2(g)
From the balanced equation, you can see that 2 moles of NaN3 are required to produce 3 moles of N2. Use the mole ratio to find the moles of sodium azide:
n(NaN3) = (3/2) * n(N2)
Finally, calculate the mass of sodium azide using the molar mass:
mass(NaN3) = n(NaN3) * molar mass(NaN3)
Substitute the given values and solve for the mass of sodium azide.