Video: Identifying the Expression for the Volume of a Gas at a Given Temperature and Pressure, Given the Initial Temperature, Pressure, and Volume

The volume of an ideal gas at 10°C and at a pressure of 750 millimeters of mercury is found to be 500 milliliters. Which of the following expressions represents the volume of the gas at 25°C and at a pressure of 720 millimeters of mercury? [A] 500 × (750/720) × (298/283) mL [B] 500 × (750/720) × (283/298) mL [C] 500 × (720/750) × (10/25) mL [D] 500 × (720/750) × (25/10) mL [E] 500 × (720/760) × (283/292) mL

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Video Transcript

The volume of an ideal gas at 10 degrees Celsius and at a pressure of 750 millimeters of mercury is found to be 500 milliliters. Which of the following expressions represents the volume of the gas at 25 degrees Celsius and at a pressure of 720 millimeters of mercury?

Our answer choices are different expressions involving the numbers given in the problem. In this question, we’re changing the properties of an ideal gas. And we want to know what will happen to the volume after these changes. Initially, the temperature of the gas is 10 degrees Celsius. The initial pressure is 750 millimeters of mercury, and the volume is 500 milliliters. The final temperature is 25 degrees Celsius. The final pressure is 720 millimeters of mercury. And the final volume is what we’re solving for.

To solve this problem, we’ll use the combined gas law. We can create an expression that we can use to solve for the final volume by multiplying both sides of the expression by the final temperature and dividing both sides by the final pressure. When we use the combined gas law, we have to use temperatures that are in units of kelvin. Our temperatures are in units of degrees Celsius. So we can convert these to kelvin by adding 273 to them. Our first temperature is 10 degrees Celsius. So in kelvin, the initial temperature is 283. The final temperature is 25 degrees Celsius. So we can convert it to kelvin by adding 273. This gives us a final temperature of 298 kelvin.

Now, we can plug everything in to create an expression for the final volume. The initial temperature is 283 kelvin. The initial pressure is 750 millimeters of mercury. The initial volume is 500 milliliters. The final temperature is 298 kelvin. And the final pressure is 728 millimeters of mercury. All of our units cancel except milliliters, which is the correct units for the final volume.

Now, let’s compare this expression we’ve created with the answer choices. In our expression, we have the numbers 750, 500, and 298 on top and 720 and 283 on the bottom. The only answer choice this matches is answer choice A, which is the correct expression to represent the volume of the gas.