Solve Combined Gas Law Problem: Volume @ STP from -247.7°C & 380 torr

[Demoniac]

Can someone explain how to solve the following problem using the Combined Gas Law step by step?

What volume will gas occupy if 60.0 mL at -247.7°C and 380 torr pressure are adjusted to STP?

Thank you.

 

[anonymity]

You are going to want to use the ideal gas equation. There is no doubt more complicated/precise ways of solving the problem, but this is how i was taught and is probably how you are expected to do so.

the equation is:

pv = nrt

where p is pressure, v is volume, n is moles, r is the ideal gas constant, and t is temperature.

the ideal gas is constant for all gasses that are assumed to behave ideally. That is, for your first condition (60.0 mL at -247.7°C and 380 torr) r will be the same as r for your second condition (stand temp and pressure).

This means that if you solve the equation for r (pv = nrt ::: r =pv / nt) you can set up a proportion of r = r, so that: p(1) * v(1) / n(1) * t(1) = p (2) * v(2) / n(2) * t(2).

With this equation you can plug in what you have (standard temp/pressure on one side, your original conditions on the other --- you will have to set up a proportion with your original data to solve for the number of moles) and solve for v(2).

You're going to have to assume that the number of moles will not change, and make sure that you keep the conditions isolated to a single side of the proportion.

-anonymous

edit: answer my question if you know it! (https://www.physicsforums.com/showthread.php?t=443314)

 

[Demoniac]

I'm sorry but I didn't understand a thing you said. Can you please explain with the combined gas law formula?

 

[Borek]

He did.

the equation is:

pv = nrt

 

[DeeNos]

To solve this problem using the Combined Gas Law, we can use the formula P1V1/T1 = P2V2/T2, where P1, V1, and T1 represent the initial pressure, volume, and temperature, and P2, V2, and T2 represent the final pressure, volume, and temperature. In this problem, we are given the initial volume (V1 = 60.0 mL) and temperature (T1 = -247.7°C) and the final pressure (P2 = 380 torr) and temperature (T2 = 273 K, which is STP). Now, we need to find the final volume (V2).

Step 1: Convert the given temperature from -247.7°C to Kelvin. To convert from Celsius to Kelvin, we add 273 to the Celsius temperature. So, T1 = (-247.7 + 273) K = 25.3 K.

Step 2: Substitute the given values into the formula. P1V1/T1 = P2V2/T2 becomes (380 torr)(60.0 mL)/(25.3 K) = (1 atm)(V2)/(273 K).

Step 3: Solve for V2 by cross-multiplying and then dividing. V2 = (380 torr)(60.0 mL)(273 K)/(1 atm)(25.3 K) = 615.6 mL.

Therefore, the final volume of the gas at STP would be 615.6 mL.