"Some Basic Concepts in Chemistry" — Practice

Question 1

A vessel contains $8$ g of methane and $8$ g of sulphur dioxide at the same temperature. Find the ratio of their partial pressures and the mole fraction of methane.

Accepted Answer

$n_{	ext{CH}_4}=\dfrac{8}{16}=0.5$ mol; $n_{	ext{SO}_2}=\dfrac{8}{64}=0.125$ mol

$\dfrac{p_{	ext{CH}_4}}{p_{	ext{SO}_2}}=\dfrac{0.5}{0.125}=4$

$x_{	ext{CH}_4}=\dfrac{0.5}{0.625}=0.8$

Methane supplies four fifths of the pressure despite contributing exactly half the mass.

Question 2

$6.0$ g of carbon is burnt in $16$ g of oxygen. Find the mass of carbon dioxide formed and identify the reagent left over.

Accepted Answer

$n_{	ext{C}}=\dfrac{6}{12}=0.5$ mol; $n_{	ext{O}_2}=\dfrac{16}{32}=0.5$ mol

The reaction needs $1:1$, so both quotients are $0.5$ and neither is in excess — the mixture is exactly stoichiometric.

$	ext{CO}_2$ formed $=0.5$ mol $=22$ g

Nothing is left over, which the mass balance confirms: $6+16=22$ g.

Question 3

A compound containing carbon, hydrogen and nitrogen gives, on analysis, $38.7\%$ C, $16.1\%$ H and $45.2\%$ N by mass. Its molar mass is $31$ g mol$^{-1}$. Find the molecular formula.

Accepted Answer

$	ext{C}: \dfrac{38.7}{12}=3.22$; $	ext{H}: \dfrac{16.1}{1}=16.1$; $	ext{N}: \dfrac{45.2}{14}=3.23$

Dividing by the smallest: $1:5:1$, giving the empirical formula $	ext{CH}_5	ext{N}$ of mass $31$.

Since the molar mass is also $31$, the molecular formula is $	ext{CH}_5	ext{N}$ — methylamine.

Question 4

A $1.5$ M aqueous solution of urea (molar mass $60$) has density $1.02$ g mL$^{-1}$. Find its molality and the mole fraction of urea.

Accepted Answer

One litre holds $1.5$ mol $=90$ g of urea and weighs $1020$ g.

Solvent mass $=1020-90=930$ g $=0.930$ kg

$m=\dfrac{1.5}{0.930}=1.61$ mol kg$^{-1}$

$n_{water}=\dfrac{930}{18}=51.7$ mol, so $x_{urea}=\dfrac{1.5}{53.2}=0.0282$

Question 5

Concentrated sulphuric acid is $98\%$ by mass with density $1.84$ g mL$^{-1}$. Find its molarity and the volume needed to prepare $500$ mL of $0.5$ M solution.

Accepted Answer

One litre weighs $1840$ g, of which $98\%$ is acid: $1803$ g.

$M=\dfrac{1803}{98}=18.4$ M

Moles required $=0.5	imes0.5=0.25$ mol

Volume $=\dfrac{0.25}{18.4}=0.0136$ L $=13.6$ mL, diluted carefully to $500$ mL.

Question 6

Find the equivalent mass of potassium dichromate as an oxidant, and the normality of a $0.05$ M solution. Its molar mass is $294$ g mol$^{-1}$.

Accepted Answer

$	ext{Cr}_2	ext{O}_7^{2-}ightarrow2	ext{Cr}^{3+}$: each chromium goes from $+6$ to $+3$, so six electrons are gained per formula unit and $n=6$.

Equivalent mass $=\dfrac{294}{6}=49$ g

$N=0.05	imes6=0.30$ N

Unlike permanganate, dichromate has the same n-factor in every medium, which is why it is preferred as a primary standard.

Question 7

$25$ mL of an oxalic acid solution requires $30$ mL of $0.1$ N sodium hydroxide for neutralisation, and separately requires $24$ mL of a permanganate solution in acid. Find the molarity of the permanganate.

Accepted Answer

As an acid, $n=2$. Equivalents in $25$ mL $=30	imes0.1=3$ meq, so the oxalic acid is $0.12$ N and $0.06$ M.

As a reductant, $	ext{C}_2	ext{O}_4^{2-}ightarrow2	ext{CO}_2$ loses two electrons, so $n=2$ again and the redox normality is also $0.12$ N.

$N_{	ext{KMnO}_4}	imes24=0.12	imes25\qquad\Rightarrow\qquad N=0.125$ N

With $n=5$ in acid, $M=\dfrac{0.125}{5}=0.025$ M.

Question 8

$0.5$ g of an iron ore is dissolved and all iron reduced to iron(II). It requires $22$ mL of $0.02$ M permanganate in acid. Find the percentage of iron in the ore.

Accepted Answer

$N_{	ext{KMnO}_4}=0.02	imes5=0.1$ N

Equivalents $=22	imes0.1=2.2$ meq $=$ equivalents of $	ext{Fe}^{2+}$

Since $n=1$ for iron(II), moles of iron $=2.2$ mmol.

Mass $=2.2	imes10^{-3}	imes56=0.1232$ g

Percentage $=\dfrac{0.1232}{0.5}	imes100=24.6\%$

Question 9

A sample of sodium hydroxide contaminated with sodium carbonate is titrated with $0.2$ N acid. Phenolphthalein gives an end point at $18$ mL and methyl orange at $24$ mL. Find the milliequivalents of each component.

Accepted Answer

$P=18$, $M=24$.

$	ext{NaOH}\equiv2P-M=36-24=12$ mL of $0.2$ N acid $=2.4$ meq

$	ext{Na}_2	ext{CO}_3\equiv2\left(M-Pight)=2\left(6ight)=12$ mL $=2.4$ meq

Since $M>P$ carbonate is present, and since $2P>M$ hydroxide is too — both consistency checks pass.

Question 10

$1.2$ g of impure magnesium carbonate is treated with $40$ mL of $0.5$ N hydrochloric acid, and the excess acid requires $10$ mL of $0.4$ N sodium hydroxide. Find the purity.

Accepted Answer

Acid added $=40	imes0.5=20$ meq

Acid left $=10	imes0.4=4$ meq

Acid consumed $=16$ meq $=$ equivalents of $	ext{MgCO}_3$

Equivalent mass $=\dfrac{84}{2}=42$, so mass $=16	imes42=672$ mg

Purity $=\dfrac{0.672}{1.2}	imes100=56\%$

Question 11

A sample of hydrogen peroxide is $11.2$ volume. Find its molarity, normality and strength in grams per litre, and the volume of oxygen released by $100$ mL at STP.

Accepted Answer

$M=\dfrac{11.2}{11.2}=1.0$ M, so $N=2.0$ N

Strength $=17	imes2=34$ g L$^{-1}$

$100$ mL releases $100	imes11.2=1120$ mL of oxygen at STP.

Check by moles: $0.1$ mol of peroxide gives $0.05$ mol of oxygen $=1.12$ L, which agrees.

Question 12

$20$ mL of a gaseous hydrocarbon requires $100$ mL of oxygen for complete combustion, and $60$ mL of carbon dioxide is formed. Identify the hydrocarbon.

Accepted Answer

Carbon: $\dfrac{60}{20}=3$ carbons per molecule.

For $	ext{C}_3	ext{H}_y$, oxygen needed per molecule is $3+\dfrac y4$, and $\dfrac{100}{20}=5$:

$3+\dfrac y4=5\qquad\Rightarrow\qquad y=8$

The hydrocarbon is $	ext{C}_3	ext{H}_8$, propane.

Practice — "Some Basic Concepts in Chemistry"

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