A solid with a density of 9 times 10^ 3 text kg m ^ -3 forms an FCC crystal with an edge length of 200sqrt 2 text pm . Calculate the molar mass of this solid. (N_A = 6 times 10^ 23 text mol ^ -1 )

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EEJ MAIN Chemistry QUESTION #7144

Question 1

A solid with a density of $9 \times 10^{3}\text{ kg m}^{-3}$ forms an FCC crystal with an edge length of $200\sqrt{2}\text{ pm}$. Calculate the molar mass of this solid. ($N_A = 6 \times 10^{23}\text{ mol}^{-1}$)

$0.0305\text{ kg mol}^{-1}$
$0.4320\text{ kg mol}^{-1}$
$0.0432\text{ kg mol}^{-1}$✔️
$0.0216\text{ kg mol}^{-1}$

Correct Answer Explanation

Using the density formula $M = \frac{d \times N_A \times a^3}{Z}$:

$d = 9000\text{ kg/m}^3$
$Z = 4$ (for FCC)
$a = 200\sqrt{2} \times 10^{-12}\text{ m}$

Calculation: $a^3 = (200\sqrt{2})^3 \times 10^{-36} = 1.6 \times 10^{-29}\text{ m}^3$.
$M = \frac{9000 \times 6 \times 10^{23} \times 1.6 \times 10^{-29}}{4} = 0.0432\text{ kg mol}^{-1}$.

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