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Question: If \[4{\text{g}}\] of \[{\text{NaOH}}\] are contained in one deciliter of solution, its molarity wou...

If 4g4{\text{g}} of NaOH{\text{NaOH}} are contained in one deciliter of solution, its molarity would be:
A.4M4{\text{M}}
B.2M2{\text{M}}
C.1M1{\text{M}}
D.1.5M1.5{\text{M}}

Explanation

Solution

To find molarity, we need to calculate moles of solute present in per litre of the solution. Moles of a substance is a SI unit of amount of substance, it can be calculated from mass, volume and number of a substance.

Complete step by step answer:
In order to find molarity of NaOH{\text{NaOH}} or sodium hydroxide, we need to first find moles of sodium hydroxide present in the given volume of solution. As the given mass of sodium hydroxide is 4g4{\text{g}} and as molar mass of sodium hydroxide means mass of 1 mole sodium hydroxide molecules and that is 40g40{\text{g}} , from this data we can easily calculate moles of sodium hydroxide and moles of a substance can be given as:
no of moles=given massmolar mass{\text{no of moles}} = \dfrac{{{\text{given mass}}}}{{{\text{molar mass}}}} ,
putting values of mass of sodium hydroxide given and molar mass of sodium hydroxide.
We get, number of moles of sodium hydroxide as: no of moles=440=0.1mol{\text{no of moles}} = \dfrac{4}{{40}} = 0.1{\text{mol}} .
Now volume of the solution can be determine from the given data in question as it is given that NaOH{\text{NaOH}} are contained in one deciliter of solution, it means volume of solution is 0.1L0.1{\text{L}} .
Now molarity of the solution is defined as the number of moles of a solute present in 1L1{\text{L}} or 1000mL1000{\text{mL}} of the solution. In our case, solute is sodium hydroxide, thereby molarity of the solution can be given as:
Molarity=moles of NaOHVolume of solution(in L)=0.10.1=1M{\text{Molarity}} = \dfrac{{{\text{moles of NaOH}}}}{{{\text{Volume of solution}}\left( {{\text{in L}}} \right)}} = \dfrac{{0.1}}{{0.1}} = 1{\text{M}} .

Thus, the correct option is C.

Note:
Molality of a solution is defined as the number of moles of solute present in 1000g1000{\text{g}} or 1kg1{\text{kg}} of a solvent. Mole fraction is the ratio of number of moles of solute or solvent present in the solution and the total number of moles present in the solution of the substance.