Question

Question #42191

Answer 1

`"2.13 atm"`

Explanation:

Your tool of choice here is the ideal gas law equation

`color(blue)(ul(color(black)(PV = nRT)))`

Here

• `P` is the pressure of the gas
• `V` is the volume it occupies
• `n` is the number of moles of gas present in the sample
• `R` is the universal gas constant, equal to `0.0821("atm L")/("mol K")`
• `T` is the absolute temperature of the gas

The most important thing to do now is to make sure that the units you have for the amount of gas present in the sample, the volume of the gas, and its temperature match the units used in the expression of the universal gas constant.

In your case, you have

`ul(color(white)(aaaacolor(black)("What you have")aaaaaaaaaacolor(black)("What you need")aaaaa))`

`color(white)(aaaaaacolor(black)("liters " ["L"])aaaaaaaaaaaaaaacolor(black)("liters " ["L"])aaaa)color(darkgreen)(sqrt())`

`color(white)(aaaaacolor(black)("moles " ["mol"])aaaaaaaaaaaaacolor(black)("moles " ["mol"])aaa)color(darkgreen)(sqrt())`

`color(white)(aaaaacolor(black)("Kelvin " ["K"])aaaaaaaaaaaaaacolor(black)("Kelvin " ["K"])aaaa)color(darkgreen)(sqrt())`

Since all the units match, you can plug them into the ideal gas law equation and find the pressure of the gas.

Rearrange the ideal gas law equation to solve for the pressure

`PV = nRT implies P = (nRT)/V`

Plug in your values to find

`P = (3.54 color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 376color(red)(cancel(color(black)("K"))))/(51.2color(red)(cancel(color(black)("L"))))`

`P = color(darkgreen)(ul(color(black)("2.13 atm")))`

The answer is rounded to three sig figs.