Final answer:
The pressure in the automobile airbag can be found using the ideal gas law. However, after calculation, the pressure does not match any of the provided options, suggesting an error in calculation or missing information in the question.
Step-by-step explanation:
To find the pressure in an automobile airbag inflated with 77.8 g of nitrogen gas at 25 °C and a volume of 66.8 L, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the grams of nitrogen to moles using the molar mass of nitrogen (N2):
77.8 g N2 × (1 mol N2 / 28.02 g N2) = 2.78 moles of N2
Next, convert the temperature to Kelvin:
T = 25 °C + 273.15 = 298.15 K
Now, we can solve for pressure:
P = (nRT) / V = (2.78 moles × 8.314 kPa·L/mol·K × 298.15 K) / 66.8 L
P = 1024.99 kPa / 66.8 L = 15.35 kPa
However, please note that none of the options a) 162 kPa, b) 217 kPa, c) 274 kPa, d) 325 kPa match the calculated pressure. The calculation seems to be off or the question might be missing some information. Therefore, please check the question parameters again to confirm the data provided is correct.