Question

6.5 moles of nitrogen gas are placed in 17.5 L container. the pressure is 1988 mmHg. what is the temperature in c? please use guess method :)

Answer 1

`-"187.74°C"`

Explanation:

First, convert pressure in `"mmHg"` to `"atm"`

`"1988 mmHg" = "1988 mmHg"/"760 mmHg/atm" = "2.6 atm"`

Use ideal gas equation

`"PV = nRT"`

`"T" = "PV"/"nR" = "2.6 atm × 17.5 L"/"6.5 mol × 0.0821 L atm / (mol K)" = "85.26 K"`

Temperature in Celsius is

`"T"_"°C" = "85.26 K" - 273 = -"187.74 °C"`

Answer 2

I guess this is the way to do it.

Explanation:

`bb(color(red)(1. "G")"iven")`

`n = "6.5 mol"`
`V = "17.5 L"`

`p = 1988 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "2.616 atm"`

`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`

`bb(color(red)(2. "U")"nknown")`

`T = "? °C"`

`bb(color(red)(3. "E")"quations")`

`pV = nRT`

`C = K-273.15`

`bb(color(red)(4. "S")"ubstitute")`

`T = (pV)/(nR) = (2.616 color(red)(cancel(color(black)("atm"))) × 17.5 color(red)(cancel(color(black)("L"))))/(6.5 color(red)(cancel(color(black)("mol"))) ×"0.082 06" color(red)(cancel(color(black)("L·atm")))·"K"^"-1"color(red)(cancel(color(black)("mol"^"-1")))) = "85.8 K"`

`C = K - 273.15 = "(85.8 - 273.15) K = -187 °C"`

`bb(color(red)(5. "S")"olve")`

`color(blue)(bar(ul(|color(white)(a/a)T = "-187 °C"color(white)(a/a)|)))" "`