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Question: The ratio of molar volume to atomic volume for 1 mole of hydrogen is (Take size of hydrogen molecul...

The ratio of molar volume to atomic volume for 1 mole of hydrogen is

(Take size of hydrogen molecule to be 1 A)

A

7.1×1047.1 \times 10^{4}

B

7.1×1067.1 \times 10^{6}

C

7.1×10107.1 \times 10^{10}

D

7.1×1087.1 \times 10^{8}

Answer

7.1×1047.1 \times 10^{4}

Explanation

Solution

Volume occupied by 1 mole of an ideal gas at STP is known as molar volume.

∴\thereforeMolar volume = 22.422.4liter =22.4×10−3m3= 22.4 \times 10^{- 3}m^{3}

Radius of hydrogen atom is r=0.5A淿˙蘂−10= 0.5A\dot{淿}蘂^{- 10}

∴\thereforeAtomic volume=43πr3NA= \frac{4}{3}\pi r^{3}N_{A}

=43×227×(0.5×10−10)3×6.023×1023=3.15×10−7m3= \frac{4}{3} \times \frac{22}{7} \times (0.5 \times 10^{- 10})^{3} \times 6.023 \times 10^{23} = 3.15 \times 10^{- 7}m^{3}

Their corresponding ratio is

MolarvolumeAtomicvolume=22.4×10−3m33.15×10−7m3=7.1×104\frac{Molarvolume}{Atomicvolume} = \frac{22.4 \times 10^{- 3}m^{3}}{3.15 \times 10^{- 7}m^{3}} = 7.1 \times 10^{4}