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Chapter 22: Problem 1

Gold has a molar (atomic) mass of \(197 \mathrm{~g} / \mathrm{mol}\). Consider a 2.56\(g\) sample of pure gold vapor. (a) Calculate the number of moles of gold present. (b) How many atoms of gold are present?

Short Answer

Expert verified
The number of moles is \(0.013\) and the number of atoms is \(7.81 \times 10^{21}\)

Step by step solution

01

Calculation of number of moles

The number of moles of a substance is given by the formula: \[ number of moles = \frac{mass of substance}{molar mass of substance}\] For gold, this becomes \[number of moles = \frac {2.56 g}{197 g/mol} \]
02

Evaluation of the number of moles

Calculate the value on the right hand side of the equation to get the number of moles.
03

Calculation of number of atoms

The number of atoms in a substance is given by the formula: \[ number of atoms = number of moles \times Avogadro's number\] Substituting the values, we get \[ number of atoms = number of moles \times 6.022 \times 10^{23} \]
04

Evaluation of the number of atoms

Calculate the value on the right hand side of the equation to get the number of atoms.

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Most popular questions from this chapter

A cylindrical container of length \(56.0 \mathrm{~cm}\) and diameter \(12.5 \mathrm{~cm}\) holds \(0.350\) moles of nitrogen gas at a pressure of \(2.05\) atm. Find the rms speed of the nitrogen molecules.

The mass of the \(\mathrm{H}_{2}\) molecule is \(3.3 \times 10^{-24} \mathrm{~g}\). If \(1.6 \times 10^{23}\) hydrogen molecules per second strike \(2.0 \mathrm{~cm}^{2}\) of wall at an angle of \(55^{\circ}\) with the normal when moving with a speed of \(1.0 \times 10^{5} \mathrm{~cm} / \mathrm{s}\), what pressure do they exert on the wall?

Consider a sample of argon gas at \(35.0^{\circ} \mathrm{C}\) and \(1.22 \mathrm{~atm}\) pressure. Suppose that the radius of a (spherical) argon atom is \(0.710 \times 10^{-10} \mathrm{~m} .\) Calculate the fraction of the container volume actually occupied by atoms.

(a) Consider \(1.00 \mathrm{~mol}\) of an ideal gas at \(285 \mathrm{~K}\) and \(1.00 \mathrm{~atm}\) pressure. Imagine that the molecules are for the most part evenly spaced at the centers of identical cubes. Using Avogadro's constant and taking the diameter of a molecule to be \(3.00 \times 10^{-8} \mathrm{~cm}\), find the length of an edge of such a cube and calculate the ratio of this length to the diameter of a molecule. The edge length is an estimate of the distance between molecules in the gas. (b) Now consider a mole of water having a volume of \(18 \mathrm{~cm}^{3}\). Again imagine the molecules to be evenly spaced at the centers of identical cubes and repeat the calculation in \((a)\).

Calculate the root-mean-square speed of smoke particles of mass \(5.2 \times 10^{-14} \mathrm{~g}\) in air at \(14^{\circ} \mathrm{C}\) and \(1.07\) atm pressure.
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