If i have 7.7 moles of gas at a pressure of 3.5 atm and at a temperature of 56°C, what is the volume of the container that the gas is in?

Answer 1

Hello, Jesus,

Use the Ideal Gas Law for this question.

PV = nRT, where n is moles and R is the gas constant.

The initial task is to pick among the many values of R to pick the one that has the units we want, so as to avoid additional conversions. Any approved value of R is valid, but converting the units is painful (e.g., from atm to another unit of pressure, such as Pascals or mmHg, just slows us down). Besides, laziness builds creativity. True story, up to a point.

The problems provides values in atm, Liters, and C. I picked the following value for R:

0.082058 L*atm*K^-1mol^-1

We'll need to convert C to K (add 273), but the other units are consistent. We will be left with liters, which is a unit of volume that will work here, since no specific unit is requested.

Rearrange the equation and to solve for V, the volume:

V = ((7.7 moles)*(0.082058 L*atm*K^-1mol^-1)*(329.15K))/(3.5 atm)

Cancel the units and see if we are left with volume:

V = ((7.7 moles)*(0.082058 L*atm*K^-1mol^-1)*(329.15K))/(3.5 atm)

V = 59.4 Liters

[Try a value of R that has different units. You'll get the same answer, but with a lot more effort getting all the conversions done correctly.]

Answer 2

Pv = nrt

v = n*r*t/p

volume = 7.7moles*.0821 L atm/ mol K * 329/3.5

volume = 59 Liters (two sig figs)