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4 years ago

8

What is the molar mass of a covalent compound if 0.486 g of it is dissolved in 25.0 ml of water and produces a freezing temperat

ure of -0.40 °c?

1 answer:

Semmy [17]4 years ago

3 0

Answer is: the molar mass of a covalent compound is 90.4 g/mol.

<span> m(compound) = 0.486 g.
m(water) = 25 mL </span>· 1 g/mL = 25 g ÷ 1000 g/kg = 0.025 kg.<span>
ΔT = 0°C - (-0.40°C) = 0.40°C.</span>

Kf(H₂O) = 1.86°C/m.

M(compound) = Kf · m(compound<span>) / m(water) · ΔT.
M</span>(compound)<span>= 1.86°C/m · 0.486 g / (0.025 kg · 0.4°C).
M</span>(compound) = 90.4 g/mol.

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(For example, the relative atomic mass of $\rm H$ is $1.008$ means that the mass of one mole of $\rm H\!$ atoms would be approximately $1.008\!$ grams on average.)

The question counted the number of $\rm H_2SO_4$ molecules without using any unit. Avogadro's Number $N_{\rm A}$ helps convert the unit of that count to moles.

Each mole of $\rm H_2SO_4$ molecules includes exactly $(1\; {\rm mol} \times N_\text{A}) \approx 6.02\times 10^{23}$ of these $\rm H_2SO_4 \!$ molecules.

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(Keep more significant figures than required during intermediary steps.)

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$\begin{aligned}& M({\rm H_2SO_4}) \\ &= (2 \times 1.008 + 32.06 + 4 \times 15.999)\; \rm g \cdot mol^{-1} \\ &= 98.702\; \rm g \cdot mol^{-1}\end{aligned}$ .

Calculate the mass of approximately $0.541389\; \rm mol$ of $\rm H_2SO_4$ :

$\begin{aligned}m &= n \cdot M \\ &\approx 0.541389\; \rm mol \times 98.702\; \rm g \cdot mol^{-1}\\ &\approx 53.3\; \rm g\end{aligned}$ .

(Rounded to three significant figures.)

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