1.13. - An Introduction to Thermal Physics

Question

A mole is approximately the number of protons in a gram of protons. The mass of a neutron is about the same as the mass of a proton, while the mass of an electron is usually negligible in comparison, so if you know the total number of protons and neutrons in a molecule(i,e., its "atomic mass"), you know the approximate mass(in grams) of a mole of these molecules. Referring to the periodic table at the back of this book ,find the mass of a mole of each of the following : Water, nitrogen (N₂), lead, quartz (S_i O₂)

Step-by-Step Solution

Answer

18g, 28g, 207.2g, 60g

Step 1 : Molar mass in the sum of atomic masses of atoms present in the molecule

Water consists of 2 hydrogen atoms & 1 oxygen atom, Hence, $m_{H_{2}O=}2m_H+1m_o$

Step 2 : Substituting the number of protons in a gram of protons.

Using the concept, hydrogen has 1g of atomic weight and oxygen has 16g  of atomic weight

m_H2O=2(1)+1(16)

m_H2O=18g

Step 3 : Similarly substituting for other molecules i,e N 2

Nitrogen has 2 nitrogen atoms

$m_{N_2}=2m_N$

$m_{N_2}=2\left(14\right)=28g$

Step 4 : Substituting for lead Pb

Lead has 1Pb atom

m_pb=1m_pb = 1(207.2)=207.2g

Step 5 : Now substituting the molar mass for quartz i.e.,SiO 2

SiO₂ has 1 silicon atom and 2 oxygen atoms

$$\begin{gathered} m_{Si{O}_2}=1m_{si}+2m_o \\ {m}_{Si{O}_2}=1\left(28\right)+2\left(16\right)=60g \end{gathered}$$