Question

Automobile air bags are inflated with nitrogen gas, which is formed by the decomposition of solid sodium azide (NaN₃). The other product is sodium metal. Calculate the volume of nitrogen gas at 27 °C and 756 torr formed by the decomposition of 125 g of sodium azide.

a) 4.50 L
b) 2.25 L
c) 6.75 L
d) 9.00 L

Answer 1

To calculate the volume of nitrogen gas formed by the decomposition of sodium azide, use the ideal gas law equation PV = nRT. Convert the temperature to Kelvin, calculate the moles of sodium azide, and substitute the values into the equation to find the volume. Option a

Step-by-step explanation:

To calculate the volume of nitrogen gas produced by the decomposition of sodium azide (NaN₃), you need to use the ideal gas law equation:

PV = nRT

Where:

P = pressure (in atm)

V = volume (in L)

n = moles

R = ideal gas constant (0.0821 L·atm/(mol·K))

T = temperature (in K)

First, convert the given temperature from °C to K:

T = 27 °C + 273.15 = 300.15 K

Next, calculate the moles of nitrogen gas produced from the given mass of sodium azide using its molar mass:

125 g NaN₃ * (1 mol NaN₃ / 65 g) = 1.923 mol NaN₃

Then, substitute the values into the ideal gas law equation:

(756 torr)(V) = (1.923 mol)(0.0821 L·atm/(mol·K))(300.15 K)

Solve for V:

V = (1.923 mol)(0.0821 L·atm/(mol·K))(300.15 K) / (756 torr) = 4.50 L

Therefore, the volume of nitrogen gas formed by the decomposition of 125 g of sodium azide at 27 °C and 756 torr is 4.50 L. Option a