A if 1 mol of a gas in a container occupies a volume of 13 l...

(a) If 1 mol of a gas in a container occupies a volume of 13 L at a pressure of 1 atm, what is the temperature of the gas in kelvins? (b) The container is fitted with a piston so that the volume can change. When the gas is heated at constant pressure, it expands to a volume of 27 L. What is the temperature of the gas in kelvins? 323.8 (c) The volume is fixed at 27 L, and the gas is heated at constant volume until its temperature is 330 K. What is the pressure of the gas? Apply the ideal gas law to each situation.

Transcript

00:01 In this problem, we have been given that there is a gas present in the container which occupies a volume of 13 liter and the number of gas present is 1 mole and provided that the pressure of the gas contained in this container, that's one atmosphere.

00:25 And we need to determine the temperature of the gas in kelvin's.

00:30 So for this, we're going to make use of the gas equation, which is pv is equal to nrt.

00:38 R is the real gas constant.

00:40 And from here, we just put the values of the variables that we have but in the si unit.

00:46 So the volume needs to be converted into cubic meters.

00:50 So that will be 13 into 10 raise to minus 3 cubic meter.

00:56 And atmosphere, we know that 1 atm is 1 .01 into 10 raise to 5.

01:03 Pascal's.

01:04 So if you put the values here, we get 1 .01 into 10 raised to 5 times 13 into 10 to minus 3.

01:11 That's equal to 1 into 8 .314.

01:15 That's the value of r times the temperature.

01:19 So from here, if we solve, we're going to get t as 1 .01 into 13 into 10 raised to 2 divided by 8 .314.

01:29 So let's simplify the numerator first.

01:32 So when we multiply 1 .01 with 13 and 100 is multiplied, we divide it by 8 .314, we get the temperature as 157 .93 kelvin.

01:48 So that's the temperature of this case in kelvin.

01:54 And in the next situation, we have been given that the same container that's fitted with a piston which can slide and the volume can definitely change because of the slide.

02:08 Now it's given that the gas if it is heated at constant pressure.

02:14 So the pressure is kept constant here.

02:17 It is observed that the gas expands to a volume which is 27 liters.

02:25 So earlier it was 13 liter and the gas expands on heating to 27 liters.

02:31 So we need to determine.

02:32 The temperature of gas in kelvin's...