How many moles of gas must be forced into a 4.4 L tire to give it a gauge pressure of 32.4 psi at 30 ∘C? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.5 psi so that the total pressure in the tire is 46.9 psi .

46.9 psi = 3.19 atmospheres.

Then use PV = nRT and solve for n

A mixture of helium, nitrogen, and oxygen has a total pressure of 763 mmHg . The partial pressures of helium and nitrogen are 244 mmHg and 190 mmHg , respectively.

What is the partial pressure of oxygen in the mixture?

To find the number of moles of gas that must be forced into the tire, we can use the ideal gas law equation:

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)

Convert the given pressure and temperature:

Pressure (in atm):
46.9 psi + 14.5 psi (atmospheric pressure) = 61.4 psi
61.4 psi = 61.4/14.7 atm ≈ 4.18 atm

Temperature (in K):
30°C + 273.15 = 303.15 K

Now, we have:
P = 4.18 atm
V = 4.4 L
R = 0.0821 L·atm/mol·K
T = 303.15 K

Rearranging the ideal gas law equation, we can solve for n:

n = PV / RT

n = (4.18 atm) * (4.4 L) / (0.0821 L·atm/mol·K) * (303.15 K)

Calculating this value gives us:

n ≈ 0.821 moles

Therefore, approximately 0.821 moles of gas must be forced into the 4.4 L tire to give it a gauge pressure of 32.4 psi at 30 °C.

To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

First, let's convert the given values to the appropriate units:
- The gauge pressure is given as 32.4 psi, but we need to consider the total pressure in the tire, which is the sum of the gauge pressure and atmospheric pressure. Therefore, the total pressure is 32.4 psi + 14.5 psi = 46.9 psi.
- The volume is given as 4.4 L.
- The temperature is given as 30 °C, but we need to convert it to Kelvin. The Kelvin temperature (T) is equal to the Celsius temperature (t) plus 273.15. So, T = 30 °C + 273.15 = 303.15 K.

Next, we need to rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)

Now, we can plug in the values into the equation:
n = (46.9 psi * 4.4 L) / (0.0821 L*atm/mol*K * 303.15 K)

Note: The gas constant in this equation is 0.0821 L*atm/mol*K, which is appropriate for this calculation.

By calculating the right side of the equation, we get:
n ≈ 2.04 moles

Therefore, approximately 2.04 moles of gas must be forced into the 4.4 L tire to give it a gauge pressure of 32.4 psi at 30 °C.