Question

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

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

Answer 1

Answer: (A)

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