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Chapter 8: Problem 45

A quantity of \(2.0 \mathrm{~g}\) of a triatomic gaseous element was found to occupy a volume of \(448 \mathrm{ml}\) at \(76 \mathrm{~cm}\) of \(\mathrm{Hg}\) and \(273 \mathrm{~K}\). The mass of its each atom is (a) \(100 \mathrm{amu}\) (b) \(5.53 \times 10^{-23} \mathrm{~g}\) (c) \(33.3 \mathrm{~g}\) (d) \(5.53\) amu

Short Answer

Expert verified
Answer: The mass of each atom of the triatomic gaseous element is \(5.53 \times 10^{-23} \mathrm{~g}\).

Step by step solution

01

Write down the given information

We are given: Mass (m) = \(2.0 \mathrm{~g}\) Volume (V) = \(448 \mathrm{ml} = 0.448 \mathrm{L}\) Pressure (P) = \(76 \mathrm{~cm}\) of Hg = 76 cm Hg × \(13.6 \frac{\mathrm{g}}{\mathrm{cm^3}} × \frac{9.81 \mathrm{m/s^2}}{1000 \mathrm{g/m^3}} × 10^4 \mathrm{~dyn/cm^2} = 1.03 × 10^6 \mathrm{~dyn/cm^2}\) Temperature (T) = \(273 \mathrm{~K}\) #forlatex#\text{Mass (m)}=2.0 \text{ g}, \text{ Volume (V)}=0.448 \text{ L}, \text{ Pressure (P)}=1.03 \times 10^6 \text{ dyn/cm}^2, \text{ Temperature (T)}=273 \text{ K}
02

Use the Ideal Gas Law

The Ideal Gas Law is given by: PV = nRT Here, n is the number of moles, R is the gas constant, and we have the values for P, V, and T. We can find the number of moles (n) by rearranging the Ideal Gas Law formula: n = PV / RT Plug in the given values and solve for n: n = \(\frac{(1.03 \times 10^6 \mathrm{~dyn/cm^2})(0.448 \mathrm{L})}{(0.0821 \mathrm{L \cdot atm/(mol \cdot K)})(273 \mathrm{~K})}\) n = 0.00600 moles of the triatomic gaseous element #forlatex#n=\frac{(1.03\times10^6\text{ dyn/cm}^2)(0.448\text{ L})}{(0.0821\text{ L}\cdot\text{atm/(mol}\cdot\text{K})(273 \text{ K})}=0.00600 \text{ moles}
03

Calculate the molar mass

Given the mass (m) and the number of moles (n), we can find the molar mass (M) using the formula: M = m/n M = \(\frac{2.0 \mathrm{~g}}{0.00600 \mathrm{~moles}}\) M = 333.3 g/mol #forlatex#\text{Molar mass (M)}=\frac{2.0\text{ g}}{0.00600 \text{ moles}}=333.3\text{ g/mol}
04

Find the mass of one atom

To find the mass of one atom, we will use Avogadro's number: Mass of one atom = \(\frac{\text{Molar Mass}}{\text{Avogadro's Number}}\) Mass of one atom = \(\frac{333.3 \mathrm{~g/mol}}{6.022 \times 10^{23} \mathrm{atoms/mol}}\) Mass of one atom = \(5.53 \times 10^{-23} \mathrm{~g}\) The mass of each atom is \(\bold{5.53 \times 10^{-23} \mathrm{~g}}\). The correct option is (b).

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Most popular questions from this chapter

The concentration of same aqueous solution of glucose is determined by two students-Sawan and Gautam. Sawan reported the concentration as \(20 \%\) (w/w) and Gautam reported the concentration as \(25 \%(\mathrm{w} / \mathrm{v}) .\) If both the concentrations are correct, then the density of solution is (a) \(0.8 \mathrm{~g} / \mathrm{ml}\) (b) \(1.0 \mathrm{~g} / \mathrm{ml}\) (c) \(1.25 \mathrm{~g} / \mathrm{ml}\) (d) \(1.33 \mathrm{~g} / \mathrm{m} 1\)

Most abundant element dissolved in sea water is chlorine at a concentration of \(19 \mathrm{~g} / \mathrm{kg}\) of sea water. The volume of earth's ocean is \(1.4 \times 10^{21} 1\). How many g-atoms of chlorine are potentially available from the oceans? Density of sea water is \(1 \mathrm{~g} / \mathrm{ml} .\left(N_{\mathrm{A}}=6 \times 10^{23}\right)\) (a) \(7.5 \times 10^{20}\) (b) \(27 \times 10^{21}\) (c) \(27 \times 10^{24}\) (d) \(7.5 \times 10^{19}\)

The volume strength of a sample of \(\mathrm{H}_{2} \mathrm{O}_{2}\) is \(8.96\) vol'. The mass of \(\mathrm{H}_{2} \mathrm{O}_{2}\) present in \(250 \mathrm{ml}\) of this solution is (a) \(0.4 \mathrm{~g}\) (b) \(27.2 \mathrm{~g}\) (c) \(6.8 \mathrm{~g}\) (d) \(108.8 \mathrm{~g}\)

Number of gas molecules present in \(1 \mathrm{ml}\) of gas at \(0^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) is called Loschmidt number. Its value is about (a) \(2.7 \times 10^{19}\) (b) \(6 \times 10^{23}\) (c) \(2.7 \times 10^{22}\) (d) \(1.3 \times 10^{23}\)

A gaseous mixture contains \(40 \% \mathrm{H}_{2}\) and \(60 \% \mathrm{He}\), by volume. What is the total number of moles of gases present in \(10 \mathrm{~g}\) of such mixture? (a) 5 (b) \(2.5\) (c) \(3.33\) (d) \(3.125\)
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