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Chapter 8: Problem 14

The atomic masses of two elements \(\mathrm{P}\) and Q are 20 and 40 , respectively. If ' \(a\) ' \(\mathrm{g}\) of \(\mathrm{P}\) contains ' \(b\) ' atoms, how many atoms are present in ' \(2 a\) ' \(\mathrm{g}\) of \(\mathrm{Q}\) ? (a) \(a\) (b) \(\underline{b}\) (c) \(2 a\) (d) \(2 b\)

Short Answer

Expert verified
Answer: 2b

Step by step solution

01

Find the number of moles for element P

To find the number of moles for element P, we will use the formula: moles = mass / atomic mass Here, mass of P = a grams and atomic mass of P = 20 So, moles of P = a / 20
02

Find the number of atoms for element P using Avogadro's number

Using Avogadro's number (6.022 x 10^23 atoms per mole), we can find the number of atoms in 'a' grams of element P. Atoms of P = moles of P × Avogadro's number b = (a / 20) × (6.022 x 10^23)
03

Find the number of moles for element Q

We will do the same for '2a' grams of element Q. mass of Q = 2a grams and atomic mass of Q = 40 So, moles of Q = (2a) / 40
04

Find the number of atoms for element Q using Avogadro's number

Using the same formula as in step 2 to find the number of atoms in '2a' grams of element Q. Atoms of Q = moles of Q × Avogadro's number = ((2a) / 40) × (6.022 x 10^23)
05

Simplify the expression for atoms of Q and compare with atoms of P

Notice that the expression for atoms of Q is half the expression for atoms of P. Since b is the number of atoms in 'a' grams of element P, then the number of atoms in '2a' grams of element Q is 2b. So, the correct answer is (d) 2b.

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Most popular questions from this chapter

Large quantities of ammonia are burned in the presence of a platinum catalyst to give nitric oxide, as the first step in the preparation of nitric acid. \(\mathrm{NH}_{3}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \stackrel{\mathrm{Pt}}{\longrightarrow} \mathrm{NO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (Unbalanced) Suppose a vessel contains \(0.12\) moles \(\mathrm{NH}_{3}\) and \(0.14\) moles \(\mathrm{O}_{2}\). How many moles of NO may be obtained?

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