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 302 K , to what pressure (in psi) can the carbon dioxide in the cartridge inflate a 3.23 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.)
turn 16 g of carbon dioxide to moles
(g/molar mass) (0.3636)
then plug into PV=nRT
P=(0.3636 moles of carbon dioxide)(0.0821)(302 temperature in kelvin)/ 3.23 volume in liters
this should equal to 2.79 atm
convert atm to psi by multiply 2.79 by 14.7
should b 41 psi, after this subtract 41 psi by 14.7
26.3 psi is the answer
Well, if you're looking to inflate your bike tire and crunching numbers, it sounds like you're tired of being deflated by flat tires! Don't worry, I'm here to help with some clownish calculations.
Now let's tackle the problem step by step. We have a volume of 3.23 L, so first, we need to convert that to liters.
3.23 L = 3.23 x 1000 mL = 3230 mL
Now, we can calculate the moles of carbon dioxide in the cartridge. To do this, we need to use the ideal gas law equation, which states PV = nRT.
Since we're looking for pressure, let's rearrange the equation: P = nRT/V
Now we know the following values:
- n (mole) = mass / molar mass
- mass = 16.0 g
- molar mass of CO2 = 44.01 g/mol (carbon dioxide)
Let's plug in those values:
n = 16.0 g / 44.01 g/mol
Now let's convert that to moles of carbon dioxide:
n = 0.363 moles (approximately)
Great! We have the moles of carbon dioxide. Now we can calculate the pressure.
P = (nRT) / V
Here's what we've got:
- R (ideal gas constant) = 0.0821 L·atm/(mol·K)
- T (temperature) = 302 K
- V (volume) = 3230 mL = 3.23 L
Plug in the values:
P = (0.363 moles x 0.0821 L·atm/(mol·K) x 302 K) / 3.23 L
After some number crunching, we find that the pressure is approximately 8.88 atm. But hold your horses, we're not done yet!
To convert atmospheres to psi, we can use the conversion factor:
1 atm = 14.7 psi
Now let's convert that pressure:
P = 8.88 atm x 14.7 psi
Lo and behold, the pressure the carbon dioxide in the cartridge can inflate the tire to is approximately 130.5 psi! That's more than enough to put some air in your bicycle tires!
But hey, remember to always stay safe and wear a helmet. After all, even the funniest clowns know the importance of safety. Happy cycling!
To find the pressure (in psi) to which the carbon dioxide can inflate the mountain bike tire, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, we need to calculate the number of moles of carbon dioxide in the cartridge. The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol.
Number of moles (n) = mass / molar mass
Number of moles (n) = 16.0 g / 44.01 g/mol ≈ 0.3635 mol
Next, we need to convert the volume of the mountain bike tire from liters to cubic meters, as the ideal gas constant (R) has units of (m^3·Pa)/(mol·K).
Volume (V) = 3.23 L = 3.23*10^(-3) m^3
Now, we can rearrange the ideal gas law equation to solve for pressure (P):
P = (nRT) / V
Substituting the known values:
P = (0.3635 mol * 8.314 J/(mol·K) * 302 K) / 3.23*10^(-3) m^3
P ≈ 86390.3 J/(mol·K) / m^3 * 302 K
P ≈ 2,612,285.4 J/m^4 * K
Finally, to convert the pressure to psi, we can use the conversion factor: 1 Pa ≈ 0.0001450377 psi.
P = 2,612,285.4 J/m^4 * K * 0.0001450377 psi/Pa
P ≈ 378.8 psi
Therefore, the carbon dioxide in the cartridge can inflate the mountain bike tire to a pressure of approximately 378.8 psi.
16.0 g CO2 is 16.0/44 = 0.354 mols.
PV = nRT
P = nRT/V = 0.354*0.08203*302/3.23 = 2.72 atm absolute
2.72 atm x (14.7 psi/1 atm) = 39.9 psi absolute
Gauge pressure = 39.9 - 14.7 = ?