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(b) Succinic acid and its salts are food additives. The formula of a molecule of succinic acid is
(CH_(2))_(n)(COOH)_(2) where
n > 1. Succinic acid reacts with sodium hydroxide according to the following balanced equation:

(CH_(2))_(n)(COOH)_(2)+2NaOHrarr(CH_(2))_(n)(COONa)_(2)+2H_(2)O
When
1.77g of succinic acid react completely with sodium hydroxide
2.43g of
(CH_(2))_(n)(COONa)_(2) (disodium succinate) are formed.
(i) Write expressions in terms of
n for the molar masses of
(CH_(2))_(n)(COOH)_(2) and
(CH_(2))_(n)(COONa)_(2).
(ii) Write expressions in terms of
n for the number of moles of succinic acid in
1.77g of the acid and the number of moles of disodium succinate in
2.43g of the salt.
(iii) Find the value of
n and the mass of one mole of succinic acid.
(iv) What volume of a
0.12MNaOH solution is required for complete reaction with an aqueous solution containing
1.77g succinic acid?

(b) Succinic acid and its salts are food additives. The formula of a molecule of succinic acid is $\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COOH})_{2}$ where $\boldsymbol{n}>1$ . Succinic acid reacts with sodium hydroxide according to the following balanced equation: $\newline$ $\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COOH})_{2}+2 \mathrm{NaOH} \rightarrow\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COONa})_{2}+2 \mathrm{H}_{2} \mathrm{O}$ $\newline$ When $1.77 \mathrm{~g}$ of succinic acid react completely with sodium hydroxide $2.43 \mathrm{~g}$ of $\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COONa})_{2}$ (disodium succinate) are formed. $\newline$ (i) Write expressions in terms of $\boldsymbol{n}$ for the molar masses of $\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COOH})_{2}$ and $\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COONa})_{2}$ . $\newline$ (ii) Write expressions in terms of $\boldsymbol{n}$ for the number of moles of succinic acid in $1.77 \mathrm{~g}$ of the acid and the number of moles of disodium succinate in $2.43 \mathrm{~g}$ of the salt. $\newline$ (iii) Find the value of $\boldsymbol{n}$ and the mass of one mole of succinic acid. $\newline$ (iv) What volume of a $\boldsymbol{n}>1$ $2$ solution is required for complete reaction with an aqueous solution containing $1.77 \mathrm{~g}$ succinic acid?

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Find a value using two-variable equations: word problems

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Q. (b) Succinic acid and its salts are food additives. The formula of a molecule of succinic acid is

\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COOH})_{2}

where

\boldsymbol{n}>1

. Succinic acid reacts with sodium hydroxide according to the following balanced equation:

\newline

\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COOH})_{2}+2 \mathrm{NaOH} \rightarrow\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COONa})_{2}+2 \mathrm{H}_{2} \mathrm{O}

\newline

When

1.77 \mathrm{~g}

of succinic acid react completely with sodium hydroxide

2.43 \mathrm{~g}

of

\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COONa})_{2}

(disodium succinate) are formed.

\newline

(i) Write expressions in terms of

\boldsymbol{n}

for the molar masses of

\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COOH})_{2}

and

\left(\mathrm{CH}_{2}\right)_{n}(\mathrm{COONa})_{2}

.

\newline

(ii) Write expressions in terms of

\boldsymbol{n}

for the number of moles of succinic acid in

1.77 \mathrm{~g}

of the acid and the number of moles of disodium succinate in

2.43 \mathrm{~g}

of the salt.

\newline

(iii) Find the value of

\boldsymbol{n}

and the mass of one mole of succinic acid.

\newline

(iv) What volume of a

\boldsymbol{n}>1

2

solution is required for complete reaction with an aqueous solution containing

1.77 \mathrm{~g}

succinic acid?

Write Expressions: Write expressions for the molar masses of $(CH_{2})_{n}(COOH)_{2}$ and $(CH_{2})_{n}(COONa)_{2}$ based on $n$ . Molar mass of $(CH_{2})_{n}(COOH)_{2}$ = $12n + 2n + 4(16) + 2(1) = 12n + 2n + 64 + 2 = 14n + 66$ g/mol. Molar mass of $(CH_{2})_{n}(COONa)_{2}$ = $12n + 2n + 2(22) + 2(16) + 2(23) = 12n + 2n + 44 + 32 + 46 = 14n + 122$ g/mol.
Calculate Moles: Calculate the number of moles of succinic acid and disodium succinate. $\newline$ Number of moles of succinic acid = mass / molar mass = $\frac{1.77\text{g}}{(14n + 66) \text{mol}}$ . $\newline$ Number of moles of disodium succinate = mass / molar mass = $\frac{2.43\text{g}}{(14n + 122) \text{mol}}$ .
Use Stoichiometry: Use the stoichiometry of the reaction to find $n$ . According to the balanced equation, $1$ mole of succinic acid produces $1$ mole of disodium succinate. Set the expressions for moles equal to each other: $\frac{1.77}{14n + 66} = \frac{2.43}{14n + 122}$ . Cross-multiply and solve for $n$ : $1.77(14n + 122) = 2.43(14n + 66)$ , $24.78n + 216.14 = 34.062n + 160.38$ , $9.282n = 55.76$ , $n = 6.01$ .

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