Question

$100$ml aqueous solution (density $=\frac{5}{3}$ g/ml) contain 40% by weight of NaOH. The number of molecules of NaOH dissolved in the above solution is :
[Use : $N_A=6\times {10}^{23}$]

• A. $2\times {10}^{22}$
• B. $3.33\times {10}^{22}$
• C. ${10}^{24}$
• D. $3.33\times {10}^{23}$

Answer 1

The correct option is C ${10}^{24}$

It is given that,

Volume of solution $=100mL$

It’s density $=\frac{5}{3}g/mL$

Concentration of NaOH is 40% of the solution.

Now, as we know that $Density=\frac{Mass}{Volume}$

Hence mass of the solution $=density\times volume=\frac{5}{3}\times 100$g

Hence, mass of NaOH$=\frac{40}{100}\times \frac{5}{3}\times 100$$=\frac{200}{3}$

Now, moles of NaOH $=GivenweightofNaOH/MolarmassofNaOH$

$=\frac{200}{3\times 40}=\frac{5}{3}$

Now number of molecules of NaOH $=numberofmoles\times N_A$

$=\frac{5}{3}\times 6\times {10}^{23}={10}^{24}$

Hence, the correct answer is (c).