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Question: If \({\text{M}}\), \({\text{W}}\), and \({\text{V}}\) represent the molar mass of the solute, mass o...

If M{\text{M}}, W{\text{W}}, and V{\text{V}} represent the molar mass of the solute, mass of the solute, and volume of the solution in litres respectively, which among the following equations is true?
A. P = M W RT V{\text{P = }}\dfrac{{{\text{M W R}}}}{{{\text{T V}}}}
B.P = T M RW V{\text{P = }}\dfrac{{{\text{T M R}}}}{{{\text{W V}}}}
C.P = T W RV M{\text{P = }}\dfrac{{{\text{T W R}}}}{{{\text{V M}}}}
D.P = T R VW M{\text{P = }}\dfrac{{{\text{T R V}}}}{{{\text{W M}}}}

Explanation

Solution

The homogeneous mixture of two or more components is called a solution while the component that is present in larger proportion is called the solvent while the component is smaller proportion is called the solute. We shall use the ideal gas equation and substitute the value of moles and rearrange the equation.

Complete step by step answer:
The solutions can be of many types. The solute and the solvent can be either solid, liquid, or gas phases. For the gas phase solutions, where the solvent is a gas and the solute is either a solid, a liquid or a gas, the solution may follow the ideal gas law equation considering the gaseous solution to behave ideally. From the ideal combined gas law equation we have,
P V = nRT{\text{P V = nRT}}
Now, the number of moles of a substance, n = WM\dfrac{{\text{W}}}{{\text{M}}}, where W{\text{W}} is the mass of the solute and M{\text{M}} is the molar mass of the solute.
Putting the value of n in the above equation, we have,
P V = WM R T{\text{P V = }}\dfrac{{\text{W}}}{{\text{M}}}{\text{ R T}}
⇒P = W R TM V \Rightarrow {\text{P = }}\dfrac{{{\text{W R T}}}}{{{\text{M V}}}}{\text{ }}

Hence, the correct answer is option C.

Note:
The concentration of the solution is measured in different units which include normality, molarity, molality, mole-fraction, etc.
The normality of the solution is the number of gram equivalents of a substance present in one litre of the solution. The molarity of the solution is the number of moles of a solute present in one litre of the solution while the molality of the solution is the number of moles of the solute present in one Kg of the solvent.