Question

A noble gas is placed in a 10.0 liter container. the noble gas has a mass of 25.25 g, the pressure is 3.05 atm, and the temperature is 24°c. find the molar mass and symbol for the gas.

Answer 1

The problem can be solved using Ideal Gas Equation.

The equation is given below.

$PV= nRT$

Step 1 : Calculate moles of the gas (n)

Where P = pressure of the gas in atm = 3.05 atm

V = Volume of the gas in Liters = 10.0 L

n = number of moles of the gas

R = Gas constant = 0.08206 L-atm/mol-K

T = Temperature of the gas in Kelvin

To convert T from Celsius to Kelvin unit, we add 273

Hence we have T = 24 + 273 = 297 K

Let us plug in the above values in ideal gas equation

$(3.05 atm) ( 10.0 L) = n (0.08206 L.atm/mol.K) ( 297 K)$

$n = \frac{(3.05atm) (10.0L)}{(0.08206 L-atm/mol) (297)}$ ... Unit K gets cancelled

$n = 1.25 mol$

Number of moles of gas are 1.25

Step 2 : Find molar mass using mol value

Mole and molar mass can be related to each other by the following expression

$Mole = \frac{Mass (grams)}{Molar mass}$

The mass of the gas is given as 25.25 g

moles (n) = 1.25 mol

After plugging the values we get,

$1.25 mol = \frac{25.25g}{Molar mass}$

Molar mass = $\frac{25.25g}{1.25mol}$

Molar mass = $20.2g/mol$

Molar mass of the gas is 20.2 /mol

Step 3 : Find identity of the gas using periodic table

From the periodic table , we can see that noble gas Neon has molar mass 20.18g/mol .

Hence the given gas is Neon which is represented by the symbol is "Ne"