Chapter 2, Problem 2.65QA

Interpretation Introduction

To find:

Moles and atoms of titanium in the given compounds

Answer to Problem 2.65QA

Solution:

a) 0.125 moles of FeTiO₃ contains 0.125 moles and 7.53 * 10²² atoms of Titanium_.

b) 0.125 moles of TiCl₄ contains 0.125 moles and 7.53 * 10²² atoms of Titanium

c) 0.125 moles of Ti₂O₃ contains 0.25 moles and 1.51 * 10²³ atoms of Titanium_.

d) 0.125 moles of Ti₃O₅ contains 0.375 moles and 2.26 * 10²³ atoms of Titanium_.

Explanation of Solution

Calculations:

a) 0.125 mol of FeTiO₃

In one molecule of FeTiO₃, there is one atom of Ti. Therefore, we can say that the mole ratio between FeTiO₃: Ti is 1:1. Now, we have the mole to mole ratio, and moles of FeTiO_3; so, we can calculate the moles of Ti using the dimensional analysis method.

$0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{T}\mathrm{i}{\mathrm{O}}_3\mathrm{ }\mathrm{*}\frac{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{T}\mathrm{i}{\mathrm{O}}_3}=0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}$

So, 0.125 mol of FeTiO₃ contains 0.125 mol of Ti.

Now, we convert moles into atoms. We know that in every 1 mol of substance we have 6.023 * 10²³ molecules or atoms of the given substance which is equal to Avogadro’s number.

$1 mol Ti = 6.023 * {10}^{23} atoms of Ti$

Using this conversion factor, we will convert 0.125 mol of Ti to atoms of Ti.

$0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}\mathrm{ }}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}=7.53\times {10}^{22} atoms of Ti$

So, 0.125 moles of FeTiO₃ contains 7.53 * 10²² atoms of Ti.

b) 0.125 mol of TiCl₄

In one molecule of TiCl₄, there is one atom of Ti. Therefore, we can say the mole ratio between TiCl₄: Ti is 1:1. Now, we have the mole to mole ratio and moles of TiCl_4; so, we can calculate the moles of Ti using the dimensional analysis method.

$0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{T}\mathrm{i}\mathrm{C}\mathrm{l}}_4\mathrm{*}\frac{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{T}\mathrm{i}\mathrm{C}\mathrm{l}}_4}=0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}$

So, 0.125 mol of TiCl₄ contains 0.125 mol of Ti.

We know that 1 mol of Ti = 6.023 * 10²³ atoms of Ti. Using this conversion factor, we will convert 0.125 mol of Ti to atoms of Ti.

$0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}\mathrm{ }\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}\mathrm{ }}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}=7.53\times {10}^{22} atoms of Ti$

So, 0.125 moles of TiCl₄ contains 7.53 * 10²² atoms of Ti.

c) 0.125 mol of Ti₂O₃

In one molecule of Ti₂O₃, there are two atoms of Ti. Therefore, we can say the mole ratio between Ti₂O₃: Ti is 1:2. Now, we have the mole to mole ratio and moles of Ti₂O_3; so, we can calculate the moles of Ti using the dimensional analysis method.

$0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_3\mathrm{*}\frac{2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}\mathrm{ }}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{ }\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_3}=0.250\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}$

So, 0.125 mol of Ti₂O₃ contains 0.250 mol of Ti.

We know that 1 mol of Ti = 6.023 * 10²³ atoms of Ti. Using this conversion factor, we will convert 0.250 mol of Ti to atoms of Ti.

$0.250\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}\mathrm{ }\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}=1.51\times {10}^{23} atoms of Ti$

So, 0.125 moles of Ti₂O₃ contains 1.51 * 10²³ atoms of Ti.

d) 0.125 mol of Ti₃O₅

In one molecule of Ti₃O₅, there are three atoms of Ti. Therefore, we can say the mole ratio between Ti₃O₅: Ti is 1:3. Now, we have the mole to mole ratio and moles of Ti₃O_5; so we can calculate the moles of Ti using the dimensional analysis method.

$0.125\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_5\mathrm{*}\frac{3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_5}=0.375\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}$

So, 0.125 mol of Ti₃O₅ contains 0.375 mol of Ti.

We know that 1 mol of Ti = 6.023 * 10²³ atoms of Ti. Using this conversion factor, we will convert 0.375 mol of Ti to atoms of Ti.

$0.375\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}\mathrm{ }\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}}= {2.26\mathrm{*}10}^{23}\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{T}\mathrm{i}$

So 0.125 moles of Ti₃O₅ contains 2.26 * 10²³ atoms of Ti.

Conclusion:

a) 0.125 moles of FeTiO₃ contains 0.125 moles and 7.53 * 10²² atoms of Titanium_.

b) 0.125 moles of TiCl₄ contains 0.125 moles and 7.53 * 10²² atoms of Titanium

c) 0.125 moles of Ti₂O₃ contains 0.250 moles and 1.51 * 10²³ atoms of Titanium_.

d) 0.125 moles of Ti₃O₅ contains 0.375 moles and 2.26 * 10²³ atoms of Titanium