How many L of N2 gas are produced at STP when an airbag inflates if the airbag contains 132g of sodium nitride?
To calculate the volume of N2 gas produced at STP when an airbag inflates, you will need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (at STP, pressure is 1 atmosphere)
V = volume
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (at STP, temperature is 273.15 K)
First, we need to determine the number of moles of N2 gas produced from the given mass of sodium nitride (Na3N). To do this, we will use the molar mass of Na3N.
The molar mass of Na3N:
(3 * atomic mass of Na) + atomic mass of N = (3 * 22.99 g/mol) + 14.01 g/mol = 85.97 g/mol
Now, calculate the number of moles of Na3N:
moles = mass / molar mass = 132 g / 85.97 g/mol ≈ 1.53 moles
Since the balanced chemical equation for the decomposition of sodium nitride predicts that 1 mole of Na3N produces 3 moles of N2, we can conclude that 1.53 moles of Na3N will produce 4.59 moles of N2 gas.
Now, we can use the ideal gas law to calculate the volume of N2 gas produced:
PV = nRT
Substituting the known values:
(1 atm) * V = (4.59 mol) * (0.0821 L·atm/(mol·K)) * (273.15 K)
Simplifying:
V = (4.59 mol) * (0.0821 L·atm/(mol·K)) * (273.15 K) / (1 atm)
V ≈ 100.2 L
Therefore, approximately 100.2 L of N2 gas are produced at STP when the airbag containing 132g of sodium nitride inflates.