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Answer :
Final answer:
To find the pressure inside an airbag inflated with nitrogen gas, we use the Ideal Gas Law. After calculations, the pressure is found to be approximately 93.1 kPa. None of options are correct.
Explanation:
To calculate the pressure of nitrogen gas inside an inflated airbag, we can apply the Ideal Gas Law equation, which is PV = nRT (where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature).
The pressure P is what we want to determine, V is given as 66.8 L (or 0.0668 m^3 for conversion into SI units), n can be found by dividing the mass of nitrogen gas by its molar mass (the molar mass of N2 is approximately 28.02 g/mol), R is the ideal gas constant with a value of 8.314 J/(mol*K), and T is the absolute temperature in Kelvin.
To convert the temperature from Celsius to Kelvin, we add 273.15 to the Celsius temperature. Hence, T = 25 °C + 273.15 = 298.15 K.
The mass of N2 is given as 77.8 g.
Calculating the number of moles (n = mass/molar mass), we have n = 77.8 g / 28.02 g/mol = 2.776 moles.
Substituting these values into the Ideal Gas Law equation, we get:
P = (nRT)/V
P = (2.776 mol x 8.314 J/(mol*K) x 298.15 K)/(0.0668 m^3)
P = 93104.55 Pa
Since 1 kPa is equivalent to 1000 Pa, to convert the pressure into kPa, we simply divide by 1000:
P = 93104.55 Pa / 1000 = 93.1 kPa
Therefore, the pressure in the bag is approximately 93.1 kPa.
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