How many moles of air must be pumped into a 4.8 L tire to give it the pressure of 47.1 psi at 25°C ? I'm not sure how to even start doing this problem.
To solve this problem, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin by adding 273.15:
T = 25°C + 273.15 = 298.15 K
Next, we need to convert the pressure from psi (pound per square inch) to atmospheres. 1 atm is equivalent to 14.7 psi. Thus:
P = 47.1 psi / 14.7 psi/atm ≈ 3.2 atm
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the known values:
n = (3.2 atm) x (4.8 L) / (0.0821 L∙atm/(mol∙K)) x (298.15 K)
Calculating this expression:
n ≈ 0.622 moles (rounded to three decimal places)
So, you would need to pump approximately 0.622 moles of air into the tire to achieve a pressure of 47.1 psi at 25°C.