Aerosol cans carry clear warnings against incineration because of the high pressures that can develop upon heating. Suppose that a can contains a residual amount of gas at a pressure of 755 mmHg and a temperature of 25 °C. What would the pressure be if the can were heated to 1155 °C?

Video transcript

Welcome back. Everyone to another video compressed air cans carry clear warnings against incineration because of the high pressures that can develop upon heating, which can cause it to explode. Suppose that a can contains a residual amount of gas at a pressure of 888 millimeters, mercury and a temperature of 39.9 °C. What would the pressure be if the can is heated to 2000 °C? And we're given four answer choices. A 8.48 B 4.80 C 9.99 and D 3.84 atmospheres. So now let's solve this problem. First of all, let's understand what's changing and what's not. So we notice that we're given pressure and temperature and those would be our variables that are changing. Since we're considering the same gas, it essentially tells us that N the number of moles R and V volume, those are not changing, they are constants. So if you think about the ideal gas law, if Nr and V are constants, and if we rearrange PV equals N RT, we end up with P divided by T equals Nr divided by V. As a result, we clearly see that P divided by T is a constant, meaning for two conditions, P one divided by T one should be equal to P two divided by T two. Now, what are we solving for? According to the problem we are solving for the final pressure P two? So if we rearrange the equation, we end up with P one divided by C one multiplied by T two. So that's all that we need. We have our setup, we're going to use the initial pressure which is 888 millimeters mercury because the answers are given in atmospheres, we're just going to immediately convert that into atmospheres knowing that one atmosphere is equivalent to 760 millimeters mercury. So we're going to use that conversion factor. OK. Well done. So we have our pressure, we're going to multiply by temperature two. We know that our final temperature is 202 I'm sorry, 2000 °C. We need to convert that into Kelvin. OK. And finally, we're going to divide everything by the initial temperature which is 39 39.9 °C. Once again, we are converting that into the absolute temperature. And when we perform our calculations, we end up with 8.48 atmospheres, which essentially corresponds to the answer choice a that would be it for today. And thank you for watching