Question

The specific heat of a certain substance is $0.86\, J\,g ^{-1} \,K ^{-1}$. Assuming ideal solution behavior, the energy required (in J) to heat $10\, g$ of $1$ molal of its aqueous solution from $300 \,K$ to $310\, K$ is closest to :
[Given: molar mass of the substance $=58\, g \,mol ^{-1}$; specific heat of water $\left.=4.2 \,J \,g ^{-1} \,K ^{-1}\right]$

• A. 401.7
• B. 424.7
• C. 420.0
• D. 86.0

Answer 1

Answer: (A)

Specific heat capacity of substance
$=0.86\, J \,g ^{-1}\, K ^{-1}$
$1$ molal aqueous solution
$\Rightarrow 1000\, gm$ water has $58\, gm$ solute
(total mass of solution $=1058\, gm$ )
If we take $10\, gm$ solution it would have
water $=\frac{1000}{1058} \times 10 \,gm$
substance $=\frac{58}{1058} \times 10\, gm$
Heat required $=\frac{1000}{1058} \times 10 \times 4.2 \times 10($ for water $)=396.975$
$+$
$\frac{58}{1058} \times 10 \times 0.86 \times 10($ for substance $)=4.715$
$=396.975+4.715=401.69 \simeq 401.7$