A 0.142 -mol sample of argon gas has a volume of 834 millilitres at a pressure of 4.83 atm. What

step 1 Hi there. This problem is another ideal gas equation problem. So that means we're going to be us

A 0.142 -mol sample of argon gas has a volume of 834...

Key Concepts

Ideal Gas Law

The ideal gas law, stated as PV = nRT, relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas using the gas constant (R). This concept is fundamental for understanding the behavior of ideal gases and allows calculation of one variable if the others are known.

Unit Conversion

In many gas law problems, converting units to the appropriate SI or consistent set is critical. For example, volume given in milliliters needs to be converted to liters, ensuring that all units match the requirements of the ideal gas law equation.

Temperature Conversion

Temperature conversion is essential when the requirement is to express temperature in a specific scale, such as converting the calculated temperature from Kelvin (the unit used in the ideal gas law) to Celsius by subtracting 273.15.

Transcript

00:01 Hi there.

00:02 This problem is another ideal gas equation problem.

00:07 So that means we're going to be using the ideal gas law, pv, equals nrt, to solve it.

00:16 Let's look at what we are given in this problem.

00:19 It appears that we are trying to find temperature in this problem.

00:26 And furthermore, we're trying to find temperature in degrees celsius.

00:31 Looking at the values that we are given, you're given a number of moles of 0 .14.

00:37 2 moles of argon, we have a volume of 834 milliliters.

00:56 I know that my universal gas constant values are in liters, so i need to convert this milliliters to liters so that units will match up.

01:06 I know that there are 1 ,000 milliliters in one liter.

01:11 So i need to take 834 and divide by a thousand to give me .834 liters.

01:21 We're also given a pressure of 4 .83 atmospheres.

01:32 Selecting my value for the universal gas constant is going to be determined by the pressure value.

01:38 The pressure value that we're given in the problem is in atmospheres.

01:41 So i'm going to select the r value that has atmospheres, and that is the 0 .0821 liters times atmospheres.

01:53 Over mole time kelvin being a constant and has some unique units.

02:00 But we'll see how that will all work out here as we calculate our answer.

02:06 So we have pv equals nrt and we've decided that we are trying to solve for t.

02:11 So i want to get t by itself.

02:15 I'm going to rearrange this equation by dividing both sides by nr.

02:21 If i divide both sides by nr, nr will disappear from this side and it'll become the denominator on that side.

02:29 So that means t is going to be equal to pv over n times r...

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