A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. c. How many moles of gas are there?

Question

Graph showing pressure vs. volume for a gas, illustrating the ideal gas law process.

Accepted Answer

Hello, everyone. Let's go through this practice problem. An ideal gas originally at a temperature of 750 degrees Celsius follows the transformation below. Calculate the amount of gas in moles. And then we're given a diagram showing the relationship between the pressure and atmospheres and the volume in liters. And we're given four multiple choice options to choose from. Option A 0.52 moles, option B 0.71 moles, option C 0.82 moles and option D 0. moles. Now, because the problem wants us to find the number of moles of the gas, we can relate that to the temperature and the pressure and the volume using the ideal gas law which states that the pressure multiplied by the volume of the gas is equal to the number of moles of the gas multiplied by the ideal gas constant multiplied by the gas temperature. To solve for the number of moles N, we can divide both sides of the equation by RT to get the N on its own. So we find that the number of moles is equal to the pressure multiplied by the volume divided by the ideal gas constant multiplied by the gasses temperature. Now, we're given the temperature t as 750 degrees Celsius in order for the ideal gas constant to work or in order for the ideal gas formula to work. However, we're going to need to use Kelvins instead. So we can convert this temperature from degrees Celsius to Kelvins by adding 273. So 273 plus 750 degrees Celsius is equal to 1023 Kelvins. So this is the value we should be using for the temperature. Also recall that the ideal gas constant R has a value of 8.314 with units of jewels per Kelvin moles. And also we need a value for pressure and volume in order for this to work. Unfortunately, for us, the graph highlights a point on the plot where the pressure and volume correspond to each other. And it tells us that the pressure as a value of four atmospheres and the volume as a value of eight liters. However, in order for us to be able to use the pressure and volume in the equation, we're going to need to get the right units instead of atmospheres for pressure, we're going to want to put that into past scales. So I'm going to do a unit conversion. So for P that's four atmospheres and we can convert this into past Kells by using the conversion factor stating that 1.13, multiplied by 10 to the power of five pascals corresponds to one atmosphere. And if you put that into a calculator, then we get a pressure of 4. multiplied by 10 to the power of five pascals. Now let's do a similar unit conversion on the eight liter volume because in order for us to use that, we want it in units of cubic meters. So eight liters and we can convert this into cubic meters using the fact that one cubic meter is equal to 1000 liters. And we find that the volume is 8. multiplied by 10 to the power of negative three cubic meters. So now all that's left for us to do is plug these values into our ideal gas law into a calculator. So to recap N is equal to PV divided by RT plugging the values into a calculator, we get 4.52 multiplied by 10 to the power of five pascals multiplied by the volume. 8.0 multiplied by 10 of the power of negative three cubic meters divided by 8. jewels per mole. Kelvin multiplied by Kelvins. And if we put this into a calculator, then we find a number of moles of about 0.38. And so that then is our answer to this problem. And if we look at our options above, we can see that this agrees with multiple choice option D 0. moles. So that is the answer to this problem and that's it. I hope this video helped you out. If you'd like to have more practice, please check out some of our other videos which will 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.

A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. c. How many moles of gas are there?

Verified Solution

Key Concepts

Ideal Gas Law

Pressure-Volume Relationship

Thermodynamic Processes