A 726 mL gas sample at STP is compressed to a volume of 117 mL, and the temperature is increased to 23◦C. What is the new pressure of the gas in Pa?
Answer in units of Pa.
I got 2.49647
The volume of a gas at 26◦C and 0.4 atm is 67 mL. What volume will the same gas sample occupy at standard conditions?
Answer in units of mL.
I got .10684
To solve these types of gas law problems, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in Pa)
V = volume (in ml)
n = number of moles
R = ideal gas constant
T = temperature (in Kelvin)
For the first question, we are given the initial and final volume, and the initial and final temperature. To find the final pressure, we can use the following steps:
1. Convert the initial and final temperatures to Kelvin:
Initial temperature = 0°C = 273K
Final temperature = 23°C = 23 + 273 = 296K
2. Convert the volumes to liters:
Initial volume = 726mL = 0.726L
Final volume = 117mL = 0.117L
3. Since the problem states that the gas is at STP (standard temperature and pressure), we know that the initial pressure is 1 atmosphere (atm).
4. Substitute the values into the ideal gas law equation and solve for the final pressure:
P1V1 / T1 = P2V2 / T2
(1atm) * (0.726L) / (273K) = P2 * (0.117L) / (296K)
P2 = (1atm * 0.726L * 296K) / (0.117L * 273K)
P2 ≈ 1.876atm
5. Convert the final pressure from atm to Pa:
1 atm = 101325 Pa (approximately)
1.876 atm ≈ 1.876 * 101325 Pa ≈ 189983.7 Pa
Therefore, the new pressure of the gas in Pa is approximately 189983.7 Pa.
For the second question, we are given the initial and final temperature, pressure, and volume. We can use the same steps outlined above to find the initial volume. Using the ideal gas law equation and following the steps:
1. Convert temperature from Celsius to Kelvin:
Temperature = 26°C = 26 + 273 = 299K
2. Convert pressure from atm to Pa:
Pressure = 0.4atm = 0.4 * 101325 Pa = 40530 Pa (approximately)
3. Substitute the values into the ideal gas law equation and solve for the initial volume:
P1V1 / T1 = P2V2 / T2
(40530Pa) * V1 / (299K) = (1atm) * (67mL) / (273K)
V1 = (1atm * 67mL * 299K) / (40530Pa * 273K)
V1 ≈ 0.109mL
4. Convert the initial volume from liters to mL:
0.109L * 1000 mL/L = 109 mL
Therefore, the volume that the same gas sample will occupy at standard conditions is approximately 109 mL.
PV = kT
So, PV/T = k, a constant.
So, you want to find P such that
117P/(273+23) = 726*1/273
Now convert that from atm to Pa
Do the other in like wise. Find V such that
1*V/273 = 0.4*67/(273+26)