Question

determine the total mass of nitrogen (n2), in kg, required to inflate all four tires of a vehicle, each to a gage pressure of 180 kpa at a temperature of 25oc. the volume of each tire is 0.6 m3, and the atmospheric pressure is 1 atm.

Answer 1

To determine the total mass of nitrogen required to inflate all four tires of a vehicle, use the ideal gas law equation. By plugging in the values and solving the equation, we find that the total mass of nitrogen required is 2.77 kg.

Step-by-step explanation:

To determine the total mass of nitrogen required to inflate all four tires of a vehicle, we need to use the ideal gas law equation: PV = nRT

Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

First, convert the gauge pressure from kPa to Pa:

180 kPa = 180,000 Pa

Next, convert the volume of each tire from m^3 to cm^3:

0.6 m^3 = 600,000 cm^3

Now we can calculate the number of moles of nitrogen. Rearranging the ideal gas law equation to solve for n:

n = PV / RT

Plugging in the values:

n = (180,000 Pa) * (600,000 cm^3) / ((8.31 J/(mol*K)) * (25+273 K))

Simplifying the equation and converting grams to kilograms, we find:

n = 98.85 mol

mass = n * molar mass of nitrogen

molar mass of nitrogen = 28 g/mol

mass = 98.85 mol * 28 g/mol * (1 kg / 1000 g) = 2.77 kg