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When 238. mg of a certain molecular compound X are dissolved in 90.0 g of benzonitrile (CHCN), the freezing point of the solution is measured to be -13.0 °C. Calculate the molar mass of X. If you need any additional information on benzonitrile, use only what you find in the ALEKS Data resource. Also, be sure your answer has a unit symbol, and is rounded to 1 significant digit. 0 8 0.2 Xx G

When 238. mg of a certain molecular compound X are dissolved in 90.0 g of benzonitrile (CHCN), the freezing point of the solution is measured to be -13.0 °C. Calculate the molar mass of X. If you need any additional information on benzonitrile, use only what you find in the ALEKS Data resource. Also, be sure your answer has a unit symbol, and is rounded to 1 significant digit. 0 8 0.2 Xx G

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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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### Calculation of Molar Mass Based on Freezing Point Depression #### Given Problem When 238 mg of a certain molecular compound X are dissolved in 90.0 g of benzonitrile (C₆H₅CN), the freezing point of the solution is measured to be -13.0 °C. Calculate the molar mass of X. #### Steps to Find Molar Mass 1. **Determine the Freezing Point Depression (ΔTf)**: - Pure benzonitrile freezing point (Tf₀): -12.82 °C - Solution freezing point (Tf): -13.0 °C - ΔTf = Tf₀ - Tf = -12.82 °C - (-13.0 °C) = 0.18 °C 2. **Use the Freezing Point Depression Formula**: ΔTf = Kf * m Where: - Kf (freezing point depression constant for benzonitrile) = 5.35 °C·kg·mol⁻¹ - m (molality) = moles of solute / kg of solvent 3. **Solve for Molality (m)**: 0.18 °C = 5.35 °C·kg·mol⁻¹ * m m = 0.18 °C / 5.35 °C·kg·mol⁻¹ m ≈ 0.03364 mol/kg 4. **Calculate Moles of Solute (compound X)**: - Mass of benzonitrile (solvent) = 90.0 g = 0.090 kg - Molality (m) = moles of X / kg of benzonitrile - Moles of X = m * kg of benzonitrile - Moles of X = 0.03364 mol/kg * 0.090 kg - Moles of X ≈ 0.0030276 mol 5. **Calculate Molar Mass (M)**: - Mass of X = 238 mg = 0.238 g - Molar mass (M) = mass of X / moles of X - Molar mass (M) = 0.238 g / 0.0030276 mol - Molar mass (M) ≈
Transcribed Image Text:### Calculation of Molar Mass Based on Freezing Point Depression #### Given Problem When 238 mg of a certain molecular compound X are dissolved in 90.0 g of benzonitrile (C₆H₅CN), the freezing point of the solution is measured to be -13.0 °C. Calculate the molar mass of X. #### Steps to Find Molar Mass 1. **Determine the Freezing Point Depression (ΔTf)**: - Pure benzonitrile freezing point (Tf₀): -12.82 °C - Solution freezing point (Tf): -13.0 °C - ΔTf = Tf₀ - Tf = -12.82 °C - (-13.0 °C) = 0.18 °C 2. **Use the Freezing Point Depression Formula**: ΔTf = Kf * m Where: - Kf (freezing point depression constant for benzonitrile) = 5.35 °C·kg·mol⁻¹ - m (molality) = moles of solute / kg of solvent 3. **Solve for Molality (m)**: 0.18 °C = 5.35 °C·kg·mol⁻¹ * m m = 0.18 °C / 5.35 °C·kg·mol⁻¹ m ≈ 0.03364 mol/kg 4. **Calculate Moles of Solute (compound X)**: - Mass of benzonitrile (solvent) = 90.0 g = 0.090 kg - Molality (m) = moles of X / kg of benzonitrile - Moles of X = m * kg of benzonitrile - Moles of X = 0.03364 mol/kg * 0.090 kg - Moles of X ≈ 0.0030276 mol 5. **Calculate Molar Mass (M)**: - Mass of X = 238 mg = 0.238 g - Molar mass (M) = mass of X / moles of X - Molar mass (M) = 0.238 g / 0.0030276 mol - Molar mass (M) ≈
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