Question

Question #51c75

Answer 1

`"6.14 moles"`

Explanation:

All you have to do here is to use the ideal gas law equation, which looks like this

`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

Rearrange the equal to solve for `n`

`PV = nRT implies n = (PV)/(RT)`

Now, before plugging in the values, make sure that he units you have for volume, pressure, and temperature match the units used in the expression of the universal gas constant.

`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)(aaacolor(black)("atmospheres " ["atm"])aaaaaacolor(black)("atmospheres " ["atm"])aaa)color(darkgreen)(sqrt())`

`color(white)(aacolor(black)("degrees Celsius " [""^@"C"])aaaaaaaaacolor(black)("Kelvin " ["K"])aaaa)color(red)(xx)`

Notice that you must convert the temperature from degrees Celsius to Kelvin. To do that, use the following conversion factor

`color(blue)(ul(color(black)(T["K"] = t[""^@"C"] + 273.15)))`

You will have

`T = 44.0^@"C" - 273.15 = "317.15 K"`

Now you're ready to solve for `n`

`n = (4.70 color(red)(cancel(color(black)("atm"))) * 34.0 color(red)(cancel(color(black)("L"))))/(0.0821 (color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * 317.15color(red)(cancel(color(black)("K"))))`

`color(darkgreen)(ul(color(black)(n = "6.14 moles")))`

The answer is rounded to three sig figs.