Answer

Verified

373.2k+ views

**Hint:**As we know that the ideal gas law is a good approximation of the behavior of various gases under certain conditions. It is a combination of the empirical Boyle's law, Charles's law, Gay-Lussac's law and Avogadro’s law. So here we have to calculate the molecular mass of the gas using the ideal gas equation.

**Formula used:**

We will use ideal gas equation (equation of state):

$PV=nRT$

$n=\dfrac{W}{M}$

where,

P = pressure of the gas

V =volume of gas it occupies

n = number of moles of gas present in the solution or sample

R = universal gas constant

T = absolute temperature of the gas

W= given mass

M =molecular mass of the gas

**Complete answer:**

Let us first discuss the ideal gas equation as follows:-

Ideal gas equation: It is the empirical relationship between volume, temperature, pressure and the amount of gas combined together into the ideal gas law which can be mathematically written as follows:-

$PV=nRT$

where,

P = pressure of the gas

V =volume of gas it occupies

n = number of moles of gas present in the solution or sample

R = universal gas constant, equal to $0.0821\dfrac{atm\cdot L}{mol\cdot K}$

T = absolute temperature of the gas

-Calculation of the moles of the gas as follows:-

The values given in the question are:-

P = 1 atm

V = 8.2L

T = 300K

On substituting all the values in ideal gas equation, we get:-

\[\begin{align}

& \Rightarrow PV=nRT \\

& \text{Rearrange the formula:-} \\

& \Rightarrow \text{n =}\dfrac{PV}{RT} \\

& \Rightarrow \text{n =}\dfrac{1atm\times 8.2L}{300K\times 0.0821\dfrac{atm\cdot L}{mol\cdot K}} \\

& \Rightarrow \text{n =}0.3329moles \\

\end{align}\]

-Calculation of molecular mass of gas using mole concept:-

The given mass (W) of gas is = 9.0g

On substituting this value in$n=\dfrac{W}{M}$, we get:-

$\begin{align}

& \Rightarrow 0.3329moles=\dfrac{9.0g}{M} \\

& \Rightarrow M=\dfrac{9.0g}{0.3329moles} \\

& \Rightarrow M=27g/mol \\

\end{align}$

**Therefore, the molecular mass of the gas is: (b) 27g/mol**

**Note:**

-Remember to change all the values with respect to universal gas constant and then use them in the formula. This will help you to get an accurate answer with minimum error.

Also there are different values of universal gas constant as shown below:-

-8.314$J\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$

-8.314${{m}^{3}}\cdot Pa\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$

-2 $cal\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$ -8.205${{m}^{3}}\cdot atm\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$

-0.082$L\cdot atm\cdot {{K}^{-1}}\cdot mo{{l}^{-1}}$

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Choose the antonym of the word given below Furious class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE