How many moles of gas must be forced into a 5.2 L tire to give it a gauge pressure of 30.6 psi at 26 ∘C? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.9 psi so that the total pressure in the tire is 45.5 psi .

To answer this question, we can use the ideal gas law, which states:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

First, let's convert the given temperatures from Celsius to Kelvin. We add 273.15 to the Celsius temperature to get the Kelvin temperature.

26 °C + 273.15 = 299.15 K

Next, we need to convert the pressure from psi to atmospheres. There are 14.7 psi in 1 atm, so we divide the given pressures by 14.7 to get the pressure in atmospheres.

P_gauge = 30.6 psi / 14.7 psi/atm = 2.08 atm
P_total = 45.5 psi / 14.7 psi/atm = 3.09 atm
P_atm = 14.9 psi / 14.7 psi/atm = 1.01 atm

Now, let's rearrange the ideal gas law equation to solve for the number of moles (n):

n = (PV) / (RT)

Substituting the values we have:

n = (2.08 atm * 5.2 L) / (0.0821 L*atm/mol*K * 299.15 K)

n = 0.246 moles of gas

Therefore, approximately 0.246 moles of gas must be forced into the tire.

I believe you should have written the 45.5 as 45.5 psia if it is 30.6 psi.

Use PV = nRT
For P convert 45.5 to atm.
Remember to convert T to kelvin.
Solve for n. Post your work if you get stuck.