0.10 mol of argon gas is admitted to an evacuated 50 cm^3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C.

a. What is the final pressure of the gas?

Question

0.10 mol of argon gas is admitted to an evacuated 50 cm^3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C.

a. What is the final pressure of the gas?

Accepted Answer

Hey, everyone. Let's go through this problem. A 0.325 mole sample of Oregon is placed in an initially empty container with a rigid non elastic walls with a volume of 440 mL. The initial temperature of the gas is 25 degrees Celsius. The gas is heated using an oven to a final temperature of 450 degrees Celsius, determine the pressure of the gas after heating. And we were given four multiple choice options to choose from. Option A 2.45 multiplied by 10 to the power of five pascals. Option B 1.83 multiplied by 10 to the power of six pascals. Option C 1.62 multiplied by 10 to the power of six pascals. And option D 4.4 multiplied by 10 to the power of six pascals. Now, for this problem, we're looking for pressure and trying to relate it to other variables like temperature volume and the number of moles in the sample. This means that we can use the ideal gas law which states that the pressure multiplied by the volume of a gas is equal to the number of moles multiplied by the ideal gas constant. R multiplied by the temperature. We're given two different temperatures in the problem. But since we're specifically looking for the pressure of the gas after the heating, we're specifically going to be focused on the higher temperature. It gives us the second temperature in the story of the problem. So piece of the final pressure multiplied by the volume of the gas. And notice, by the way is a side note that the, the problem tells us that the container has rigid non elastic walls, meaning that the volume is constant. So the final pressure multiplied by the volume of the container is equal to the number of moles multiplied by the ideal gas constant multiplied by the final temperature. So T sub F, since we're trying to solve for pressure, let's divide both sides of the equation by volume to solve for P sub F. And we find that piece of F is equal to N RT sub F divided by the volume. Now let's take a look at the variables we've been given. We're told that the final temperature T sub F is equal to 450 degrees Celsius. In order for our units to be consistent, we'll have to add 273 to convert this into Kelvins. So our final temperature is actually equal to 723 Kelvins. We also want to convert the, the units for the volume we're given because we're told that the volume of the of the tank is 440 mL. Unfortunately, because 1 mL is equal to 1 cc. This is also equal to 440 cubic centimeters. And to convert this into meters, let's apply a unit conversion. So 1 m for 100 centimeters and the whole thing is being cubed. So this is then equal to a volume of 4.4 multiplied by 10 to the power of negative four cubic meters. Now let's plug all of this into our equation for the pressure. So piece of F is equal to N, the number of moles which the problem tells us is 0.3 to five moles, 0.3 to five moles. Then we multiply r the ideal gas constant and recall that the ideal gas constant is equal to 8.314 jewels per mole. Kelvin multiplied by the final temperature which we established earlier is 723 Kelvins. And we divide all of this by the volume which we just established a moment ago is 4.4 multiplied by 10 to the power of a negative four cubic meters. So if we put all of this into a calculator, then we find a final pressure of about 4.4 multiplied by 10 to the power of six pascals. And this is the final pressure. So this is the answer to this problem. And if we look at our multiple choice options, we can see that this agrees with option D. So the correct answer to this problem is option D 4.4 multiplied by 10 to the power of six past scouts. And that is it for this problem. I hope this video helps you out. If you'd like more practice, please check out some of our other videos which will hopefully give you more experience with these types of problems, but that's all for now. And I hope you all have a lovely day. Bye bye.

0.10 mol of argon gas is admitted to an evacuated 50 cm^3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. a. What is the final pressure of the gas?

Verified Solution

Key Concepts

Ideal Gas Law

Isochoric Process

Temperature Conversion