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Calculate the mass of the solute in the ...

Calculate the mass of the solute in the following solutions :
(i) `100 cm^(3)` of `N/10 KOH`
(ii) `150 cm^(3)` of `M/2 HCl`

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To calculate the mass of the solute in the given solutions, we will follow these steps for each part of the question. ### Part (i): Calculate the mass of solute in `100 cm³` of `N/10 KOH` 1. **Convert the volume from cm³ to liters**: \[ 100 \, \text{cm}^3 = 100 \, \text{mL} = 0.1 \, \text{L} \] 2. **Identify the normality and the molar mass of KOH**: - Normality (N) = \( \frac{1}{10} \) N = 0.1 N - Molar mass of KOH = 56 g/mol 3. **Use the formula for normality**: \[ \text{Normality} = \frac{\text{Gram equivalent of solute}}{\text{Volume of solution in L}} \] Rearranging gives: \[ \text{Gram equivalent of solute} = \text{Normality} \times \text{Volume of solution in L} \] Substituting the values: \[ \text{Gram equivalent of solute} = 0.1 \, \text{N} \times 0.1 \, \text{L} = 0.01 \, \text{equivalents} \] 4. **Calculate the number of moles of KOH**: Since KOH releases one OH⁻ ion, the number of equivalents is equal to the number of moles: \[ \text{Moles of KOH} = 0.01 \, \text{moles} \] 5. **Calculate the mass of KOH**: Using the formula: \[ \text{Mass} = \text{Moles} \times \text{Molar mass} \] Substituting the values: \[ \text{Mass of KOH} = 0.01 \, \text{moles} \times 56 \, \text{g/mol} = 0.56 \, \text{g} \] ### Part (ii): Calculate the mass of solute in `150 cm³` of `M/2 HCl` 1. **Convert the volume from cm³ to liters**: \[ 150 \, \text{cm}^3 = 150 \, \text{mL} = 0.15 \, \text{L} \] 2. **Identify the molarity and the molar mass of HCl**: - Molarity (M) = \( \frac{1}{2} \) M = 0.5 M - Molar mass of HCl = 36.5 g/mol 3. **Use the formula for molarity**: \[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in L}} \] Rearranging gives: \[ \text{Moles of solute} = \text{Molarity} \times \text{Volume of solution in L} \] Substituting the values: \[ \text{Moles of solute} = 0.5 \, \text{M} \times 0.15 \, \text{L} = 0.075 \, \text{moles} \] 4. **Calculate the mass of HCl**: Using the formula: \[ \text{Mass} = \text{Moles} \times \text{Molar mass} \] Substituting the values: \[ \text{Mass of HCl} = 0.075 \, \text{moles} \times 36.5 \, \text{g/mol} = 2.7375 \, \text{g} \approx 2.73 \, \text{g} \] ### Final Answers: - (i) Mass of KOH in 100 cm³ of N/10 KOH = **0.56 g** - (ii) Mass of HCl in 150 cm³ of M/2 HCl = **2.73 g**
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