A motorist discovers that her auto tire measures 29.2 psi rather than the recommended 35 psi. If the tire’s volume is assumed constant at 11.6 L and the temperature is 45F at the filling station, how many moles of air will the motorist need to add to bring the tire to 35 psi? (assume 1.00 atm = 14.7 psi)

  0.20 moles

Explanation:

The pressure is proportional to the quantity of gas at a given temperature and volume. So, the quantity needs to be increased by a factor of ...

  (35 psi)/(29.2 psi) = 175/146 ≈ 1.19863

The fractional increase required is ...

  1.19863 -1 = 0.19863

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The quantity of air currently in the tire is ...

  1 mol·519.67°R/(atm·23.6442 L) × (29.2/14.7 atm) × (11.6 L) / (45+459.67)°R

  = 1.0035 mol

so we need to add ...

  (fraction to add) × (current quantity) = amount to add

  0.19863 × 1.0035 mol = 0.1993 mol = amount to add

About 0.20 moles of air must be added to the tire to bring the pressure up.