The enthalpies of neutralization of a weak acid (HA) and a week acid (HB) by NaOH are -6900 cal/equivalent and -2900 cal/equivalent, respectively. When one equivalent of NaOH is added to a solution containing one equivalent of HA and one equivalent of HB, the enthalpy change was -3900 cal. If the base is distributed between HA and HB in the ratio of 1 : x, then the value of x is _____.

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answer is 3.

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Detailed Solution

(3)
Sol. $\underset{z}{H A} + \underset{z}{N a O H} \to N a A + H_{2} O$
   $\underset{y}{H B} + \underset{y}{N a O H} \to N a B + H_{2} O$
z + y = 1
   $\frac{z}{y} = \frac{1}{x}, y = x z$
   $z + x z = 1, z (1 + x) = 1$
   $z = \frac{1}{1 + x}$
   $(6900 \times \frac{1}{1 + x}) + (2900 \times \frac{x}{1 + x}) = 3900$
   $6900 + 2900 x = 3900 + 3900 x$
3000 = 1000 x, x = 3

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