Question

A sample of helium gas is heated at constant pressure from 373 k to 873 k. the final volume of the sample is 9.0 l. what was the initial volume of the gas?

Answer 1

The final volume of the sample is 18.15 L.

Step-by-step explanation:

To solve this problem, we can use the ideal gas law equation:

P1V1/T1 = P2V2/T2

Given: P1 = 0.75 atm, V1 = 17.5 L, T1 = 298 K, T2 = 303 K, P2 = 0.987 atm

Plugging in the values:

(0.75 atm)(17.5 L)/(298 K) = (0.987 atm)(V2)/(303 K)

Solving for V2:

V2 = (0.75 atm)(17.5 L)(303 K)/(0.987 atm)(298 K) = 18.15 L

The final volume of the sample is 18.15 L.

Answer 2

The initial volume = 3.86 liters

Step-by-step explanation:

We can use the combined gas law:

P1V1/T1 = P2V2/T2

where P, V, and T are Pressure, Volume, and Temperature at the initial (1) and final (2) conditions. Temperature must be in units of Kelvin.

We want to find P1, the initial volume. Rearrange to isolate P1:

V1 = V2(P2/P1)(T1/T2)

Nopte the manner in which I organize the right side: the variables are expressed as ratios of the before and after conditions. This makes it easier to:

1. See what changes in P and T will do to V1, and
2. Make it easier to cancle trhe units, and insure they are in units that match (e.g., both are in atm and K, for example).
3. Mkaes it easier predict an approximate outcome, as a means to check the calculation step.

Putting in the data:

V1 = V2(P2/P1)(T1/T2)

Since P1 = P2 (constant pressure) (P2/P1) = 1

V1 = (9L)(1)(373K/873K)

We can see that the final answer should be les than 9 liters. An approximate guess may be made by saying (373K/873K) is close to 1/2 (a bit below 1/2)/. So we'd predict the initial volume will be under to 4.5 liters.

Do the calculation to find that V1 = 3.86 liters. This is a reasonable match to our guess of under 4.5 liters. Does this answer make sense? The gas was being heated at constant pressure, so one would expect it to expand, just as in a balloon. Yes, it makes sense.

So I'm moving on to the next problem.