15gm of substance is dissolved in 450ml of water the resulting solution was found to freeze at -0.34degree Celsius.Calculate the molar mass of the substance.
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To calculate the molar mass of the substance, we need to use the freezing point depression equation:
ΔT = Kf * m
Where:
ΔT is the change in temperature (from the freezing point of the pure solvent to the freezing point of the solution)
Kf is the cryoscopic constant for the solvent (water)
m is the molality of the solution (moles of solute per kilogram of solvent)
In this problem, we know the change in temperature (ΔT = -0.34°C) and the molality of the solution (15 g of solute in 450 g of water).
First, convert the mass of the solute to moles:
Moles of solute = mass of solute / molar mass of solute
Since we are trying to find the molar mass of the solute, we'll keep it as 'M'.
Moles of solute = 15 g / M
Next, we need to find the molality of the solution:
Molality = moles of solute / kg of solvent
Since we have 450 g of water, which is equivalent to 0.450 kg:
Molality = (15 g / M) / 0.450 kg = (15 / M) / 0.450
Now, plug these values into the freezing point depression equation:
-0.34°C = Kf * ((15 / M) / 0.450)
The cryoscopic constant for water (Kf) is 1.86°C/m.
-0.34°C = 1.86°C/m * ((15 / M) / 0.450)
Simplify the equation:
-0.34 = 1.86 * (15 / M) / 0.450
Multiply both sides by 0.450:
-0.34 * 0.450 = 1.86 * (15 / M)
-0.153 = 27.9 / M
Now, cross-multiply:
-0.153M = 27.9
Divide both sides by -0.153:
M = 27.9 / -0.153
M ≈ -182.35
The molar mass should be a positive value, so we made a mistake somewhere. Please double-check your calculations and units to find the error.