Question

When 5.42 g of a certain molecular compound X are dissolved in 80.0 g of formamide (NH, COH), the freezing point of the solution is measured to be -1.4 °C. Calculate the molar mass of X. If you need any additional information on formamide, use only what you find in the ALEKS Data resource. Also, be sure your answer has a unit symbol, and is rounded to 2 significant digits. One x 6 ?

Answer 1

Answer : The molar mass of X is 72 g/mol.

Explanation : Given,

Mass of X (solute) = 5.42 g

Mass of formamide (solvent) = 80.0 g = 0.080 kg

Molar mass of formamide = 45.04 g/mole

Formula used :

`\Delta T_f=i* K_f* m\\\\T^o-T_s=i* K_f*\frac{\text{Mass of compound X}}{\text{Molar mass of compound X}* \text{Mass of formamide in Kg}}`

where,

`\Delta T_f` = change in freezing point

`\Delta T_s` = freezing point of solution =
`-1.4^oC`

`\Delta T^o` = freezing point of formamide =
`2.2^oC`

i = Van't Hoff factor = 1 (for no-electrolyte)

`K_f` = freezing point constant for formamide =
`3.85^oC/m`

m = molality

Now put all the given values in this formula, we get

`[2.2-(-1.4)]^oC=1* (3.85^oC/m)* \frac{5.42g}{\text{Molar mass of compound X}* 0.080kg}`

`\text{Molar mass of compound X}=72.4g/mol\approx 72g/mol`

Therefore, the molar mass of X is 72 g/mol.

Answer 2

Molecular mass of X is 73g/mol

Step-by-step explanation:

To answer this question you need to know that Freezing-point depression (A colligative property) is the decrease of the freezing point of a solvent on the addition of a non-volatile solute. The formula is:

ΔT = Kf m

Where ΔT is the freezing point depression (2,57°C - (-1,4°C) = 3,97°C Where 2,57°C is the melting point of formamide.

Kf that is freezing point molar constant of the solvent (4,25°C/m)

And m that is molality (moles of solute/kg of solvent). Replacing:

m =
`(3,97)/(4,25) =0,934 m`

Knowing you have 80,0g of solvent ≡ 0,0800 kg:

0,934 mol solute/kg solvent×0,08 kg solvent = 0,07472 moles of solute ≡ moles X

As grams of X are 5,42, molecular mass of X is:

`(5,42g)/(0,07472 moles)` = 73 g/mol

I hope it helps!