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Chapter 8: Problem 25

The density of a DNA sample is \(1.1 \mathrm{~g} / \mathrm{m} 1\) and its molar mass determined by cryoscopic method was found to be \(6 \times 10^{8} \mathrm{~g} / \mathrm{mole}\). What is the volume occupied by one DNA molecule? \(\left(N_{\mathrm{A}}=6 \times 10^{23}\right)\) (a) \(5.45 \times 10^{8} \mathrm{ml}\) (b) \(1.83 \times 10^{-9} \mathrm{~m} 1\) (c) \(9.06 \times 10^{-16} \mathrm{ml}\) (d) \(1.09 \times 10^{-13} \mathrm{ml}\)

Short Answer

Expert verified
Answer: (d) \(1.09 \times 10^{-13} \mathrm{ml}\)

Step by step solution

01

Calculate the Number of Moles of the DNA Sample

First, we need to calculate the mass of one DNA molecule. We are given the molar mass of the DNA sample which tells us the mass of 1 mole of DNA. To find the mass of one DNA molecule, we will divide the molar mass by Avogadro's number: Mass of one DNA molecule = \(\frac{6 \times 10^{8} \mathrm{~g} / \mathrm{mole}}{6 \times 10^{23}}\)
02

Calculate the Volume of One DNA Molecule

Now that we have the mass of one DNA molecule, we can use the density formula to find the volume occupied by one DNA molecule. The density formula is: Density = \(\frac{mass}{volume}\) We are given the density of the DNA sample, so we can rearrange the formula to solve for volume: Volume of one DNA molecule = \(\frac{Mass of one DNA molecule}{Density of DNA sample}\) Substitute the values for mass of one DNA molecule and density of DNA sample: Volume of one DNA molecule = \(\frac{\frac{6 \times 10^{8} \mathrm{~g} / \mathrm{mole}}{6 \times 10^{23}}}{1.1 \mathrm{~g} / \mathrm{m} 1}\)
03

Calculate the Volume Occupied by One DNA Molecule and Choose the Correct Answer

With all the values in place, we can now calculate the volume occupied by one DNA molecule: Volume of one DNA molecule = \(1.09 \times 10^{-13} \mathrm{ml}\) Looking at the options given, our answer is: (d) \(1.09 \times 10^{-13} \mathrm{ml}\)

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Most popular questions from this chapter

Iron form two oxides. If for the same mass of iron, mass of oxygen combined in the first oxide is two-third of the mass of oxygen combined in the second oxide, the ratio of valency of iron in first and second oxide is (a) \(1: 1\) (b) \(2: 3\) (c) \(3: 2\) (d) \(2: 5\)

Equal masses of oxygen, hydrogen and methane are taken in identical conditions. What is the ratio of the volumes of the gases under identical conditions? (a) \(16: 1: 8\) (b) \(1: 16: 2\) (c) \(1: 16: 8\) (d) \(2: 16: 1\)

A compound has carbon, hydrogen, and oxygen in \(3: 3: 1\) atomic ratio. If the number of moles in \(1 \mathrm{~g}\) of the compound is \(6.06 \times 10^{-3}\), the molecular formula of the compound will be (a) \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{O}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{2}\) (c) \(\mathrm{C}_{9} \mathrm{H}_{9} \mathrm{O}_{3}\) (d) \(\mathrm{C}_{12} \mathrm{H}_{12} \mathrm{O}_{4}\)

One molecule of haemoglobin will combine with four molecules of oxygen. If \(1.0 \mathrm{~g}\) of haemoglobin combines with \(1.642 \mathrm{ml}\) of oxygen at body temperature \(\left(27^{\circ} \mathrm{C}\right)\) and a pressure of 760 torr, what is the molar mass of haemoglobin? (a) \(6,00,000\) (b) \(1,50,000\) (c) 15,000 (d) 60,000

A quantity of \(5 \mathrm{~g}\) of a crystalline salt when rendered anhydrous lost \(1.8 \mathrm{~g}\) of water. The formula mass of the anhydrous salt is 160 . The number of molecules of water of crystallization in the salt is (a) 3 (b) 5 (c) 2 (d) 1
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