Answer :

Final answer:

To calculate the pressure in the air bag, we can use the ideal gas law equation. for hence, option (b) is the correct answer.

Explanation:

The pressure in the air bag can be calculated using the ideal gas law equation, which is PV = nRT. Where P is the pressure V is the volume. n is the number of moles. R is the ideal gas constant. T is the temperature. We are given the volume and the temperature, and we need to calculate the pressure in kPa. Rearranging the equation, we have P = (nRT) / V. Substituting the given values, we can calculate the pressure.

To find the pressure of the nitrogen gas in the air bag, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin. First, we convert the given temperature to Kelvin by adding 273.15 to 25 °C, giving us 298.15 K. Then, we use the molar mass of nitrogen (28.02 g/mol) to convert the mass (77.8 g) to moles.

n = mass / molar mass = 77.8 g / 28.02 g/mol = 2.776 moles. Now we can use the ideal gas law to solve for P:
P = (nRT) / V
P = [(2.776 mol) × (8.314 J/(mol·K)) × (298.15 K)] / (66.8 L × 103 to convert L to m3)
P = (72911.996 J) / (66.8 m³)Since 1 J = 1 Pa·m3, then P in Pascals (Pa) can be converted to kilopascals (kPa) by dividing by 1000.
P in kPa = 72911.996 Pa / 1000 = 72.912 kPa

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