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

20.2 g/mol; Ne

Step-by-step explanation:

Answer 2

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 = ((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 = (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 = (25.25g)/(Molar mass)`

Molar mass =
`(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"