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Chapter 8: Problem 38

The volume of one mole of water at \(277 \mathrm{~K}\) is \(18 \mathrm{ml}\). One \(\mathrm{ml}\) of water contains 20 drops. The number of molecules in one drop of water will be \(\left(N_{\mathrm{A}}=6 \times 10^{23}\right)\) (a) \(1.07 \times 10^{21}\) (b) \(1.67 \times 10^{21}\) (c) \(2.67 \times 10^{21}\) (d) \(1.67 \times 10^{20}\)

Short Answer

Expert verified
(a) \(1.67 \times 10^{22}\) (b) \(3.33 \times 10^{22}\) (c) \(6.67 \times 10^{22}\) (d) \(1.33 \times 10^{23}\) Answer: (a) \(1.67 \times 10^{22}\)

Step by step solution

01

Find the number of moles in 1 ml of water

We know that one mole of water occupies a volume of \(18 \mathrm{ml}\) at \(277 \mathrm{K}\). To find the number of moles in \(1 \mathrm{ml}\) of water, we can use the ratio of volumes: $$ \text{Number of moles in 1 ml} = \frac{1 \mathrm{_~ml}}{18 \mathrm{~ml}} $$
02

Calculate the number of molecules in 1 ml of water

Now that we have the number of moles in \(1 \mathrm{ml}\) of water, we can find the total number of molecules present in \(1 \mathrm{ml}\) using Avogadro's number: $$ \text{Number of molecules in 1 ~ml} = \text{Number of moles in 1 ~ml} \times N_{\mathrm{A}} $$
03

Find the number of molecules in 1 drop of water

We know that there are 20 drops in \(1 \mathrm{ml}\) of water. To find the number of molecules in one drop, we can divide the total number of molecules in \(1 \mathrm{ml}\) by the number of drops: $$ \text{Number of molecules in 1 drop} = \frac{\text{Number of molecules in 1 ~ml}}{20} $$
04

Calculate and choose the correct answer

Putting all the values, we get: $$ \text{Number of molecules in 1 drop} = \frac{1}{18} \times N_{\mathrm{A}} \times \frac{1}{20} = \frac{1}{18 \times 20} \times 6 \times 10^{23} $$ Now, calculate this value and choose the option that matches the calculated result.

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Most popular questions from this chapter

A volume of \(200 \mathrm{ml}\) of oxygen is added to \(100 \mathrm{ml}\) of a mixture containing \(\mathrm{CS}_{2}\) vapour and \(\mathrm{CO}\), and the total mixture is burnt. After combustion, the volume of the entire mixture is \(245 \mathrm{ml}\). Calculate the volume of the oxygen that remains (a) \(67.5 \mathrm{ml}\) (b) \(125.0 \mathrm{ml}\) (c) \(200.0 \mathrm{ml}\) (d) \(100.0 \mathrm{ml}\)

Two successive reactions, \(\mathrm{A} \rightarrow \mathrm{B}\) and \(\mathrm{B} \rightarrow \mathrm{C}\), have yields of \(90 \%\) and \(80 \%\) respectively. What is the overall percentage yield for conversion of \(\mathrm{A}\) to \(\mathrm{C}\) ? (a) \(90 \%\) (b) \(80 \%\) (c) \(72 \%\) (d) \(85 \%\)

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A quantity of \(0.25 \mathrm{~g}\) of a substance when vaporized displaced \(50 \mathrm{~cm}^{3}\) of air at \(0^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm} .\) The gram molecular mass of the substance will be (a) \(50 \mathrm{~g}\) (b) \(100 \mathrm{~g}\) (c) \(112 \mathrm{~g}\) (d) \(127.5 \mathrm{~g}\)

The vapour density of a sample of \(\mathrm{SO}_{3}\) gas is 28 . Its degree of dissociation in to \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) is (a) \(1 / 7\) (b) \(1 / 6\) (c) \(6 / 7\) (d) \(2 / 5\)
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