Question

Question #dd0b7

Answer 1

`"17,000 Pa"`

Explanation:

The first thing you need to do here is to convert the number of molecules of sulfur dioxide to moles by using Avogadro's constant

`color(blue)(ul(color(black)("1 mole SO"_2 = 6.022 * 10^(23)color(white)(.)"molecules SO"_2)))`

In your case, the sample will contain

`1 * 10^(22) color(red)(cancel(color(black)("molecules SO"_2))) * "1 mole SO"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules SO"_2))))`

`= "0.0166 moles SO"_2`

Next, use the ideal gas law equation to find the pressure of the gas in atmospheres.

`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.

Rearrange to solve for `P`

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

Plug in your values to find the pressure of the gas -- keep in mind that you must convert the temperature from degrees Celsius to Kelvin

`P = (0.0166 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")))) * (273.15 + 27)color(red)(cancel(color(black)("K"))))/(2.5color(red)(cancel(color(black)("L"))))`

`P = "0.164 atm"`

Finally, convert this to pascals by using the conversion factor

`color(blue)(ul(color(black)("1 atm = 101,325 Pa")))`

You will end up with

`0.164 color(red)(cancel(color(black)("atm"))) * "101,325 Pa"/(1color(red)(cancel(color(black)("atm")))) = color(darkgreen)(ul(color(black)("17,000 Pa")))`

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one significant figure for the number of molecules of sulfur dioxide.