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In 100ml , 0.1N Na2CO3.xH2O solution. Ma...

In 100ml , 0.1N `Na_2CO_3.xH_2O` solution. Mass of solute is 1.43g, then value of X is:

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To solve the problem, we need to find the value of \( x \) in the compound \( Na_2CO_3 \cdot xH_2O \) given the mass of solute and the normality of the solution. Here’s a step-by-step solution: ### Step 1: Understand the given data - Volume of solution = 100 mL - Normality (N) = 0.1 N - Mass of solute (Na2CO3·xH2O) = 1.43 g ### Step 2: Calculate the number of equivalents The formula to calculate the number of equivalents is: \[ \text{Number of equivalents} = \frac{N \times V}{1000} \] Where: - \( N \) = Normality - \( V \) = Volume in mL Substituting the values: \[ \text{Number of equivalents} = \frac{0.1 \times 100}{1000} = 0.01 \text{ equivalents} \] ### Step 3: Relate equivalents to moles The number of equivalents can also be expressed as: \[ \text{Number of equivalents} = \text{moles} \times n \] Where \( n \) is the n-factor. For \( Na_2CO_3 \), the n-factor is 2 (since it can donate 2 moles of \( Na^+ \) ions or accept 2 moles of \( CO_3^{2-} \) ions). Thus: \[ 0.01 = \text{moles} \times 2 \] From this, we can find the number of moles: \[ \text{moles} = \frac{0.01}{2} = 0.005 \text{ moles} \] ### Step 4: Calculate the molar mass Using the formula for moles: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \] We can rearrange this to find the molar mass: \[ \text{molar mass} = \frac{\text{mass}}{\text{moles}} = \frac{1.43 \text{ g}}{0.005 \text{ moles}} = 286 \text{ g/mol} \] ### Step 5: Set up the equation for molar mass The molar mass of \( Na_2CO_3 \cdot xH_2O \) can be calculated as: \[ \text{Molar mass of } Na_2CO_3 + x \times \text{Molar mass of } H_2O \] The molar mass of \( Na_2CO_3 \) is: \[ (2 \times 23) + 12 + (3 \times 16) = 46 + 12 + 48 = 106 \text{ g/mol} \] The molar mass of \( H_2O \) is 18 g/mol. Therefore, the molar mass of \( Na_2CO_3 \cdot xH_2O \) is: \[ 106 + 18x \] ### Step 6: Set up the equation We can equate the two expressions for molar mass: \[ 106 + 18x = 286 \] ### Step 7: Solve for \( x \) Rearranging the equation: \[ 18x = 286 - 106 \] \[ 18x = 180 \] \[ x = \frac{180}{18} = 10 \] ### Conclusion The value of \( x \) is 10.
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