A $100 m L$ solution was made by adding $1.43 g$ of ${Na}_{2} {CO}_{3} . {xH}_{2} O$ .The normality of the solution is $0.1 N$ . The value of $x$ is ________. (The atomic mass of $N a$ is $23 g / m o l$ ).

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Solution

Step 1: Calculate the number of gram equivalents of ${Na}_{2} {CO}_{3} . {xH}_{2} O$
Molar mass of ${Na}_{2} {CO}_{3} . {xH}_{2} O = (23 \times 2) + 12 + (16 \times 3) + 18 x = 106 + 18 x$
Number of gram equivalents of ${Na}_{2} {CO}_{3} . {xH}_{2} O = (\frac{1.43}{106 + 18 x}) \times 2$
Step 2: Calculate the value of $x$
Normality, $N = 0.1 = \frac{(\frac{1.43}{106 + 18 x}) \times 2}{\frac{100}{1000}}$
$\Rightarrow 106 + 18 x = 286 \Rightarrow x = 10$
Thus, the value of $x$ is $10$ .

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