Question

Question #c1c9e

Answer 1

The approximate temperature is 20 °C.

To solve this problem, we can use the Ideal Gas Law

`PV = nRT`.

In the formula, `P` is the pressure, `V` is the volume, `n` is the number of moles of gas, `R` is the Universal Gas Constant, and `T` is the Kelvin temperature.

We want to solve the Ideal Gas Law for `T`.

To get `T` by itself, we must divide both sides of the equation by `nR`:

`PV = nRT`

`(PV)/(nR)` = `(nRT)/(nR)`

`(PV)/(nR) = T`.

Thus,

`T = (PV)/(nR)`

Substituting values, we get

`T = (PV)/(nR) = (0.987"atm" × 12"L")/(0.50"mol" × 0.082 06"L·atm·K⁻¹mol⁻¹")` = 290 K

Notice how the units cancel to give the temperature in kelvins.

Now we convert to the Celsius temperature:

290 K = (290 - 273.15)°C ≈ 20 °C

Note: I have calculated the answer to only 1 significant figure, because the number of moles and the volume had only 2 significant figures.

The calculated Kelvin temperature had only 2 significant figures. When we subtracted 273.15, we lost one of these significant figures. If you need more precision, you will have to recalculate.