A sample of gas occupies 135 mL at 22.5^∘ C ; the pressure is 165 torr. What is the pressure of

A sample of gas occupies 135 mL at 22.5^∘ C ; the pressure...

A sample of gas occupies $135 \mathrm{~mL}$ at $22.5^{\circ} \mathrm{C} ;$ the pressure is 165 torr. What is the pressure of the gas sample when it is placed in a $252-\mathrm{mL}$ flask at a temperature of $0.0^{\circ} \mathrm{C} ?$

Key Concepts

Combined Gas Law

The combined gas law relates the pressure, volume, and temperature of a fixed amount of gas through the relationship P1V1/T1 = P2V2/T2. This law is particularly useful when a gas sample undergoes changes in more than one state variable (pressure, volume, or temperature) and it assumes that the quantity of gas remains constant throughout the process.

Temperature Conversion to Kelvin

Gas law equations require temperatures to be expressed on an absolute scale, hence the conversion of Celsius to Kelvin is essential. Kelvin is obtained by adding 273.15 to the Celsius temperature, ensuring that the temperature measurements are in a suitable scale for direct proportionality in gas law calculations.

Pressure Unit Conversion

In gas law problems, consistency of pressure units is vital. Pressures provided in units such as torr often need to be converted to a common unit like atmospheres or pascals to maintain consistency when performing calculations within the gas law equations.

Transcript

00:01 With this question, we have to look at the fact that we're dealing with an ideal gas and we're taking the same sample of gas and we're not changing the number of moles of gas.

00:13 So under changing conditions, this is going to utilize what's known as the combined gas law.

00:22 So looking at changing pressure, volume, and temperature, while moles are held constant, we get a combined gas law of p1 v1 over t1 equals p2 v2 over t2.

00:42 And an easier way to kind of isolate your variables and look at what you need is to go ahead and cross multiply so that you get p1 v1 t2 equals p2 v2 times t1.

01:01 And this actually by the way works for anytime you're changing the conditions because whatever you have that's being held constant you can cross off.

01:11 So you know with that you can even add in moles if you were looking at something with moles which would be p1 v1 over n1 t1 equals p2 v2 over n2 t2.

01:27 And if you cross multiply then you just cross off whatever is held constant then you know you can use that.

01:33 Once you look at keeping that you're only describing a single gas that you're not changing the conditions of, then you'll use the whole pivot.

01:42 Now in here notice that we're not using r.

01:46 So since we're not using r, as long as our units agree, we can use any units of volume or pressure.

01:53 But for all gases temperature does have to be in kelvin.

01:58 So we're going to add 273 here to get 295 .5 for kelvin and then this is going to be 273 kelvin...

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