Question
Calculate the molar mass of a compound if 15.0 g dissolved in 70 g of ethanol
(kb = 1.22 oC/m) caused the boiling point of ethanol to increase from 78.5 oC
to 84 oC.
(kb = 1.22 oC/m) caused the boiling point of ethanol to increase from 78.5 oC
to 84 oC.
Answers
GPT 3.5
To calculate the molar mass of the compound, we need to use the formula:
ΔT = (m * Kb) / (molar mass * molality)
Where:
ΔT = change in boiling point
m = mass of compound dissolved in solvent (ethanol)
Kb = boiling point elevation constant
molality = moles of solute / mass of solvent (ethanol)
First, let's find the molality of the solution:
Mass of solvent (ethanol) = 70 g
Molar mass of ethanol (C2H5OH) = 46.07 g/mol
Moles of solvent (ethanol) = mass of solvent / molar mass of ethanol = 70 g / 46.07 g/mol = 1.52 mol
molality = moles of solute / mass of solvent (ethanol)
molality = (15.0 g / molar mass) / 70 g
Now, let's calculate ΔT:
ΔT = change in boiling point = boiling point after - boiling point before = 84 °C - 78.5 °C = 5.5 °C
We can rearrange the formula to solve for the molar mass:
molar mass = (m * Kb) / (ΔT * molality)
Substituting the given values:
molar mass = (15.0 g * 1.22 °C/m) / (5.5 °C * (15.0 g / molar mass) / 70 g)
To simplify the expression, let's cancel out the units:
molar mass = (15.0 * 1.22) / (5.5 * (15.0 / molar mass) / 70)
molar mass = 18.3 / (5.5 * (1.0 / molar mass) / 70)
Let's simplify further by multiplying the fractions:
molar mass = 18.3 * (70 / 5.5) * molar mass / 1.0
molar mass = 18.3 * (70 / 5.5)
molar mass = 234.5454 g/mol
Therefore, the molar mass of the compound is approximately 234.55 g/mol.
ΔT = (m * Kb) / (molar mass * molality)
Where:
ΔT = change in boiling point
m = mass of compound dissolved in solvent (ethanol)
Kb = boiling point elevation constant
molality = moles of solute / mass of solvent (ethanol)
First, let's find the molality of the solution:
Mass of solvent (ethanol) = 70 g
Molar mass of ethanol (C2H5OH) = 46.07 g/mol
Moles of solvent (ethanol) = mass of solvent / molar mass of ethanol = 70 g / 46.07 g/mol = 1.52 mol
molality = moles of solute / mass of solvent (ethanol)
molality = (15.0 g / molar mass) / 70 g
Now, let's calculate ΔT:
ΔT = change in boiling point = boiling point after - boiling point before = 84 °C - 78.5 °C = 5.5 °C
We can rearrange the formula to solve for the molar mass:
molar mass = (m * Kb) / (ΔT * molality)
Substituting the given values:
molar mass = (15.0 g * 1.22 °C/m) / (5.5 °C * (15.0 g / molar mass) / 70 g)
To simplify the expression, let's cancel out the units:
molar mass = (15.0 * 1.22) / (5.5 * (15.0 / molar mass) / 70)
molar mass = 18.3 / (5.5 * (1.0 / molar mass) / 70)
Let's simplify further by multiplying the fractions:
molar mass = 18.3 * (70 / 5.5) * molar mass / 1.0
molar mass = 18.3 * (70 / 5.5)
molar mass = 234.5454 g/mol
Therefore, the molar mass of the compound is approximately 234.55 g/mol.
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