Two moles of an ideal gas originally at 380 torr and 298 K are compressed at constant temperature to a final pressure of 680 torr. Use the ideal gas law to calculate the volumes of gas at the initial and final pressures.
Question
Two moles of an ideal gas originally at 380 torr and 298 K are compressed at constant temperature to a final pressure of 680 torr. Use the ideal gas law to calculate the volumes of gas at the initial and final pressures.
Solution
Sure, let's use the ideal gas law to solve this problem. The ideal gas law is 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.
Step 1: Convert the pressures from torr to atm because the gas constant R is usually defined with pressure in atm. 1 atm = 760 torr, so 380 torr = 380/760 = 0.5 atm and 680 torr = 680/760 = 0.895 atm.
Step 2: Use the ideal gas law to find the initial volume (V1). We know that n = 2 moles, R = 0.0821 L atm/(mol K), and T = 298 K. So, we can plug these values into the ideal gas law:
0.5 atm * V1 = 2 moles * 0.0821 L atm/(mol K) * 298 K
Solving for V1 gives V1 = (2 moles * 0.0821 L atm/(mol K) * 298 K) / 0.5 atm = 48.6 L.
Step 3: Use the ideal gas law again to find the final volume (V2) at the final pressure of 0.895 atm:
0.895 atm * V2 = 2 moles * 0.0821 L atm/(mol K) * 298 K
Solving for V2 gives V2 = (2 moles * 0.0821 L atm/(mol K) * 298 K) / 0.895 atm = 27.3 L.
So, the volume of the gas decreases from 48.6 L to 27.3 L when it is compressed at constant temperature from 380 torr to 680 torr.
Similar Questions
The typical formula for the ideal gas law is = .Where represents volume, represents number of moles, is the absolute temperature, is the gas pressure and is the ideal gas constant.
A 0.250 mole sample of an ideal gas has a volume of 0.00200 m3, a pressure of 2.00 atmospheres. What is the temperature of the sample of gas?
A quantity of 2.00 mol of an ideal gas is maintained at a temperature of 127ûC in a containerof volume 0.083 m3 . What is the pressure of the gas?
Complete the following statements:a. At constant volume and number of moles, the pressure of an ideal gas as the temperature decreases according to .b. At constant temperature and number of moles, the volume of an ideal gas as the pressure decreases according to .c. At constant temperature and pressure, the volume of an ideal gas as the number of gas atoms or molecules increases according to .
One mole of oxygen gas is at a pressure of 6.50 atm and a temperature of 28.5°C.(a) If the gas is heated at constant volume until the pressure triples, what is the final temperature? °C(b) If the gas is heated so that both the pressure and volume are doubled, what is the final temperature? °C
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.