Question

The temperature of $5$ mL of a strong acid increases by $5^o$C when $5$ mL of a strong base is added to it. If $10$ mL of each is mixed, temperature should increase by:

• A. $5^o$C
• B. ${10}^o$C
• C. ${15}^o$C
• D. cannot be known

Answer 1

The correct option is A $5^o$C

Let the concentration of strong acid and a strong base is c M.

For the reaction $H^{+}+O{H}^{-}\to H_{2}O$

1 mol of acid reacts with 1 mol of base to give 1 mol of water and generated heat H J

Thus, on mixing 5 mL i.e $5c\times {10}^{-3}$mol of each, amount of heat generated =$H\times 5c\times {10}^{-3}J$

Also, heat generated $q=m.C_p\Delta T$

where m=mass of solution, C=specific heat of water, $\Delta T$=temperature change. let the density of solution =$\rho g/mL$

For 5 mL of each acid and base:

$H\times 5c\times {10}^{-3}J=\rho \times (5+5)\times C\times \Delta T_1$

$\Delta T_1=\frac{H5c\times {10}^{-3}}{10C\rho }$

$\Delta T_1=\frac{Hc}{2C\rho }\times {10}^{-3}$

Similarly for 10 mL of each acid and base solution :

$H\times 10cmJ=\rho \times (10+10)\times C\times \Delta T_2$

$\Delta T_2=\frac{10cH}{20C\rho }\times {10}^{-3}$

$\Delta T_2=\frac{Hc}{2C\rho }\times {10}^{-3}$

Thus $\Delta T_1=\Delta T_2$

In general,

Reaction of strong acid with strong base is a neutralization reaction. The enthalpy change for neutralization of strong acid and strong base is constant an has a value of -57.1 kJ/mol.

$H^{+}+O{H}^{-}\to H_{2}O;{\Delta }_{neut}{H}^0=-56.1kJ/mol$

The temperature of 5 ml of a strong acid increases by $5^{\circ }C$ when 5 ml of a strong base is added to it. If 10 ml of each is mixed, temperature should increase by $5^{\circ }C$.