Question

Question #8b6ce

Answer 1

By using the Ideal Gas Law equation (`PV = nRT`)

Explanation:

Look at the given, you were given the Pressure (P), Temperature (T), Volume (V) and mass (m) of an unknown gas.

P = 79.97 kPa
V = 4.167 L
T = `30^@C`
m= 20.83 g

Based on the given, you can definitely use the Ideal Gas Law equation to find the molar mass of the gas, where R is a constant equal to `0.0821 (L*atm)/(mol*K)`.

But first, we need to convert units:
P = `79.97 cancel "kPa"` x `(0.00986923 atm)/(1 cancel "kPa")` = `0.789 atm`
V = `4.167 L`
T = `30^@C` + `273.15 K` = `303.15 K`
m= `"20.83 g"`

Now we are ready to compute.

`PV = nRT`

`(0.789 atm) (4.167 L)` = `n` (`0.0821 (L*atm)/(mol* cancel K)`) (`303.15 cancel K`)

`"3.288 atm"*L` = `n` (`24.8583 (L*atm)/(mol)`)

n = `(3.288 cancel "atm"* cancel L)/(24.8583 cancel L* cancel (atm)/"mol")` = 0.1322 mol

Since molar mass is defined as weight of substance over the number of moles substance or

MM = `("g substance")/("mol substance")`

then

MM = `("20.83 g")/("0.1322 mol")`

MM = `color (red) (157.56 g/"mol")`

Therefore, the molar mass of the unknown gas is 157.56 g/mol.