How many moles of gas must be forced into a 5.0 L tire to give it a gauge pressure of 33.6 psi at 28 ∘C? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.8 psi so that the total pressure in the tire is 48.4 psi .
PV = nRT
48.4 x 5.0 = n x .0821 x 301K
9.79 mol
The formula shown is correct.
The temperature was correctly converted to Kelvin as well.
You need to convert the psi to atm.
Psi to atm formula = Total pressure/ atmospheric pressure
48.4/14.8 = 3.2703
14.8 atm x 5.0 = n x 0.0821 x 301K
74 = 24.7121
74/24.71 = 2.99 mol
(please dislike if this is wrong.)
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 = moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
In this case, the gauge pressure is given as 33.6 psi and the atmospheric pressure is 14.8 psi. Therefore, the total pressure in the tire is 48.4 psi.
We can convert the pressures from psi to atmospheres by dividing by 14.7 (1 atm = 14.7 psi), which gives us:
P_total = (48.4 psi) / (14.7 psi/atm) = 3.29 atm
The volume is given as 5.0 L, and the temperature is given as 28°C, which we need to convert to Kelvin.
T = 28°C + 273 = 301 K
Now we can plug these values into the Ideal Gas Law equation:
(P_total)(V) = (n)(R)(T)
(3.29 atm)(5.0 L) = (n)(0.0821 L·atm/mol·K)(301 K)
Solving for n:
n = (3.29 atm * 5.0 L) / (0.0821 L·atm/mol·K * 301 K)
n ≈ 9.79 mol
Therefore, approximately 9.79 moles of gas must be forced into the 5.0 L tire to give it a gauge pressure of 33.6 psi at 28°C.
To calculate 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 is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we are given the gauge pressure of 33.6 psi, but we need to convert it to absolute pressure by adding the atmospheric pressure of 14.8 psi. So, the total pressure in the tire is 48.4 psi.
We are also given the volume of the tire as 5.0 L and the temperature as 28 °C. However, we need to convert the temperature to Kelvin by adding 273 to get 301 K.
Plugging these values into the ideal gas law equation:
48.4 psi * 5.0 L = n * 0.0821 L·atm/(mol·K) * 301 K
Simplifying the equation:
242 L·psi = 24.7381 n mol·atm
Now, solve for n by dividing both sides of the equation by 24.7381 mol·atm:
n = (48.4 psi * 5.0 L) / (0.0821 L·atm/(mol·K) * 301 K)
n ≈ 9.79 mol
Therefore, approximately 9.79 moles of gas must be forced into the tire to achieve a gauge pressure of 33.6 psi at 28 °C.