Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (c) At what temperature would the pressure in the tank equal 15.2 MPa?

Video transcript

Hey everyone in this example, we're told that a gas container with the volume 300 liters contains five bars of nitrogen gas at 20 degrees Celsius. We need to calculate the temperature at which our nitrogen gas in the container is 8. bars. So we want to recall that for this type of question. We're going to use dig a loose tax law where we take our initial pressure, divide that by our initial temperature and set that equal to our final pressure divided by our final temperature. For the purpose of solving this question, we're going to reorganize this law so that we have our initial pressure multiplied by the final pressure set equal to our final pressure, multiplied by our initial temperature. And what we would have plugging in the info from the prompt is our initial pressure given as five bars from the question. Were then multiplying this by our final temperature, which is what we need to solve for. So that's T two Set equal to our final pressure given in the prompt as 8.60 bars. And then multiplied by our initial temperature given in the prompt as 20°C. However, we want this to be in Kelvin. So we're going to add to 73.15. So simplifying this, we would have five bars. Our initial pressure multiplied by the final temperature of our container equal to a value of the product of the right hand side, which is going to equal 2521.09. And our units are now bars, times kelvin. So we want to go ahead and isolate for the final temperature by dividing both sides by five bars. And so this allows us to cancel our units of bars, leaving us with Kelvin as our final unit, which is what we want for temperature and what we're going to get is that our final temperature of our container is equal to a value of 504. Kelvin. Now, we want to go ahead and convert this back to Celsius. So we're going to subtract 2 73.15 and this is going to give us our final answer in Celsius of 31 point oh seven degrees Celsius as our final temperature of our container. And this is going to be our final answer to complete this example. So I hope that everything I went through is clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.