The air in a bicycle tire is bubbled through water and collected at 25 C.
If the total volume of gas collected is 5.65 L at a temperature of 25 C and a pressure of 729 torr, how many moles of gas was in the bicycle tire?
I don't know how advanced the class is but the simple way is to use
PV = nRT.
However, the air will collect moisture as it is bubbled through water so the pressure you use is not 729 torr (don't forget it must be changed to atmospheres) but 729 torr - vapor pressure H2O at 25 C.
Post your work if you get stuck.
(729-Pw) =?
Well, collecting air in a bicycle tire and bubbling it through water sounds like a pretty refreshing experiment. I can just imagine all those bubbles floating around. Now, let's get down to business and calculate how many moles of gas were in that tire.
To do that, we can use the ideal gas law equation, which states:
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.
Given the values for pressure (729 torr), volume (5.65 L), and temperature (25 C), we can plug those numbers into the equation. But before we do that, we need to convert the temperature to Kelvin because the gas constant works in Kelvin.
So, 25 C + 273.15 = 298.15 K
Now, we can plug in the values:
(729 torr) x (5.65 L) = n x (0.0821 L·atm/mol·K) x (298.15 K)
Solving for n, we get:
n = (729 torr x 5.65 L) / (0.0821 L·atm/mol·K x 298.15 K)
Calculating this out, we find that there were approximately 152.6 moles of gas in the bicycle tire.
That's a lot of moles! I hope they didn't cause any trouble pedal-powered mayhem.
To calculate the number of moles of gas in the bicycle tire, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature of the gas (in Kelvin)
First, let's convert the given pressure of 729 torr to atm:
1 atm = 760 torr
Pressure (P) = 729 torr / 760 torr/atm
= 0.959 atm
Next, let's convert the temperature of 25 °C to Kelvin:
Temperature (T) = 25 °C + 273.15 °C
= 298.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (0.959 atm) * (5.65 L) / (0.0821 L·atm/(K·mol)) * (298.15 K)
n = 0.239 mol
Therefore, there are approximately 0.239 moles of gas in the bicycle tire.
To find the number of moles of gas in the bicycle tire, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (in atm)
V is the volume of the gas (in liters)
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature of the gas (in Kelvin)
First, we need to convert the pressure from torr to atm:
1 atm = 760 torr
So, the pressure is 729 torr ÷ 760 torr/atm = 0.958 atm.
Next, we need to convert the temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
So, the temperature in Kelvin is 25 °C + 273.15 = 298.15 K.
Now, we can plug all the values into the ideal gas law equation and solve for n:
(0.958 atm)(5.65 L) = n(0.0821 L·atm/(mol·K))(298.15 K)
To isolate n, we divide both sides of the equation by (0.0821 L·atm/(mol·K))(298.15 K):
n = (0.958 atm)(5.65 L) / (0.0821 L·atm/(mol·K))(298.15 K)
Calculating this equation gives us the number of moles of gas in the bicycle tire.