Pressurized carbon dioxide inflators can be used to inflate a bicycle tire in the event of a flat. These inflators use metal cartridges that contain 16.0 g of carbon dioxide. At 295 K, to what pressure (in psi) can the carbon dioxide in the cartridge inflate a 3.15-L mountain bike tire? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi. Ignore the volume of the cartridge.)
I honestly have no clue how to approach this question. Some tips just to get started would be super appreciated.
p = pressure in tire = 14.7 + pgage
CO2 = 12 + 32 = 44 grams/mol
so 16 g = .364 mol of CO2
so n = .364
T = 295 deg K
V = 3.15 Liters
then
p V = n R T
get that p and subtract 1 atm to get gage
Well, the first tip I can give you is to always approach problems with a little bit of humor. After all, laughter is the best pressure reliever! Now, let's tackle this question together.
To start, we need to convert the given mass of carbon dioxide (16.0 g) into moles. So, let's do a little "mole" dance. One mole of any gas occupies 22.4 liters at standard temperature and pressure (STP).
16.0 g of carbon dioxide is approximately equal to 0.363 moles. How, you ask? Well, I called up Avogadro, and he whispered it in my ear.
Now, let's consider the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is temperature in Kelvin.
We know the volume (3.15 L) and the temperature (295 K), but we're trying to solve for pressure. However, we need to consider the gauge pressure, which is the pressure relative to atmospheric pressure.
So, let's subtract atmospheric pressure (14.7 psi) from the total pressure we want to find, which we'll call P_total.
Now, rearrange the ideal gas law equation to solve for P_total:
P_total = (nRT/V) + atmospheric pressure
Plug in the values:
P_total = (0.363 mol * 0.0821 L·atm/mol·K * 295 K) / 3.15 L + 14.7 psi
And one more step: convert the units from atm to psi, because we're all about versatility:
P_total = 9.17 psi + 14.7 psi
P_total = 23.87 psi
Voila! The carbon dioxide in the cartridge can inflate your bike tire to approximately 23.87 psi. Just remember, it's always good to have a little extra pressure in reserve, just like a good joke up your sleeve!
To solve this question, you can use the ideal gas law, which states that 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.
First, you need to determine the number of moles of carbon dioxide in the cartridge. This can be done using the molar mass of carbon dioxide.
1. Convert the mass of carbon dioxide from grams to moles.
- The molar mass of carbon dioxide (CO2) is 44.01 g/mol.
- Divide the mass (16.0 g) by the molar mass (44.01 g/mol) to find the number of moles.
Next, you need to determine the pressure (gauge pressure) once the carbon dioxide is released into the tire.
2. Rearrange the ideal gas law to solve for P.
- P = (nRT) / V
- Substitute the values:
- n: the number of moles of carbon dioxide from step 1
- R: the ideal gas constant (0.0821 L·atm/(mol·K))
- T: the temperature in Kelvin (295 K)
- V: the volume of the mountain bike tire (3.15 L)
3. Calculate the pressure (gauge pressure) in atm.
- Substitute the values into the equation and calculate P in atmospheres.
4. Finally, convert the pressure from atm to psi.
- 1 atm = 14.7 psi (approximately)
- Multiply the pressure in atmospheres by 14.7 to get the pressure in psi.
Follow these steps, and you should be able to solve the problem step-by-step.
To solve this question, we need to apply the ideal gas law equation. The ideal gas law equation is given by:
PV = nRT
where:
P = pressure in pascals (Pa)
V = volume in cubic meters (m^3)
n = number of moles of gas
R = ideal gas constant (8.31 J/(mol·K))
T = temperature in Kelvin (K)
We can rearrange this equation to solve for pressure:
P = (nRT) / V
Given that we have 16.0 g of carbon dioxide, we need to first convert this mass to moles. The molar mass of carbon dioxide (CO2) is approximately 44.0 g/mol.
n = mass / molar mass
n = 16.0 g / 44.0 g/mol
Next, we need to convert the volume from liters to cubic meters.
V = 3.15 L = 3.15 x 10^-3 m^3
Now, we can substitute the values into the equation to calculate the pressure:
P = ((nRT) / V)
However, keep in mind that the pressure we obtain from this equation will be the absolute pressure. To find the gauge pressure, we need to subtract the atmospheric pressure of 14.7 psi.
I hope these tips help you get started with solving the question!