QuestionMay 5, 2025

10. What is the molality of a solid solution containing 0.125 g of chromium and 81.3g of iron?

10. What is the molality of a solid solution containing 0.125 g of chromium and 81.3g of iron?
10. What is the molality of a solid solution containing 0.125 g of chromium and 81.3g of iron?

Solution
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Answer

The molality of the solution is approximately 0.0296 mol/kg. Explanation 1. Understand Molality Molality is defined as the number of moles of solute per kilogram of solvent. It is expressed in units of mol/kg. 2. Calculate Moles of Solute (Chromium) First, we need to calculate the number of moles of chromium. The atomic mass of chromium (Cr) is approximately 51.996 g/mol. Using the formula for moles: \[ \text{Moles of Cr} = \frac{\text{mass of Cr}}{\text{molar mass of Cr}} = \frac{0.125 \, \text{g}}{51.996 \, \text{g/mol}} \] Calculating this gives: \[ \text{Moles of Cr} \approx 0.002404 \, \text{mol} \] 3. Convert Mass of Solvent (Iron) to Kilograms The mass of iron (Fe), which acts as the solvent, needs to be converted from grams to kilograms: \[ 81.3 \, \text{g} = 0.0813 \, \text{kg} \] 4. Calculate Molality Now, using the definition of molality: \[ \text{Molality} = \frac{\text{moles of solute}}{\text{kilograms of solvent}} = \frac{0.002404 \, \text{mol}}{0.0813 \, \text{kg}} \] Calculating this gives: \[ \text{Molality} \approx 0.0296 \, \text{mol/kg} \]

Explanation

1. Understand Molality<br /> Molality is defined as the number of moles of solute per kilogram of solvent. It is expressed in units of mol/kg.<br /><br />2. Calculate Moles of Solute (Chromium)<br /> First, we need to calculate the number of moles of chromium. The atomic mass of chromium (Cr) is approximately 51.996 g/mol. Using the formula for moles:<br />\[<br />\text{Moles of Cr} = \frac{\text{mass of Cr}}{\text{molar mass of Cr}} = \frac{0.125 \, \text{g}}{51.996 \, \text{g/mol}}<br />\]<br />Calculating this gives:<br />\[<br />\text{Moles of Cr} \approx 0.002404 \, \text{mol}<br />\]<br /><br />3. Convert Mass of Solvent (Iron) to Kilograms<br /> The mass of iron (Fe), which acts as the solvent, needs to be converted from grams to kilograms:<br />\[<br />81.3 \, \text{g} = 0.0813 \, \text{kg}<br />\]<br /><br />4. Calculate Molality<br /> Now, using the definition of molality:<br />\[<br />\text{Molality} = \frac{\text{moles of solute}}{\text{kilograms of solvent}} = \frac{0.002404 \, \text{mol}}{0.0813 \, \text{kg}}<br />\]<br />Calculating this gives:<br />\[<br />\text{Molality} \approx 0.0296 \, \text{mol/kg}<br />\]
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