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Chapter 9: Problem 182

Succinic acid, an intermediate in the metabolism of certain foods, has a molecular mass of \(118.1 \mathrm{~g} / \mathrm{mole}\). A \(1.926 \mathrm{~g}\) sample of succinic acid \(\left(\mathrm{H}_{x} \mathrm{Suc}\right)\) reacts with exactly \(1.25 \mathrm{~g}\) of \(\mathrm{NaOH}\) according to the following balanced equation: \(\mathrm{H}_{x} \mathrm{Suc}+x \mathrm{NaOH} \rightarrow \mathrm{Na}_{x} \mathrm{Suc}+x \mathrm{H}_{2} \mathrm{O}\) What is the value of \(x\) ?

Short Answer

Expert verified
The value of x is approximately \(2\), which means that 2 moles of NaOH react with 1 mole of succinic acid in the given reaction.

Step by step solution

01

Calculate the moles of succinic acid

To find the moles of succinic acid, use the given mass of the sample and its molar mass: Moles of succinic acid = (Mass of succinic acid) / (Molar Mass of succinic acid) Moles of succinic acid = \( \frac{1.926 g}{118.1 g/mol} \)
02

Calculate the moles of NaOH

Similarly, we need to find the moles of NaOH using its given mass and molar mass: Moles of NaOH = (Mass of NaOH) / (Molar Mass of NaOH) Molar Mass of NaOH = 22.99 g/mol (Na) + 15.999 g/mol (O) + 1.00784 g/mol (H) = 40.00 g/mol Moles of NaOH = \( \frac{1.25 g}{40.00 g/mol} \)
03

Find the stoichiometric ratio

In the balanced equation: \( \mathrm{H}_{x} \mathrm{Suc} + x \mathrm{NaOH} \rightarrow \mathrm{Na}_{x} \mathrm{Suc} + x \mathrm{H}_{2} \mathrm{O} \) For every mole of succinic acid, x moles of NaOH react. So, to find the value of 'x', we need to find the stoichiometric ratio: x = Moles of NaOH / Moles of succinic acid Now, let's plug in the values from step 1 and 2:
04

Calculate the value of x

x = \( \frac{ \frac{1.25}{40} }{ \frac{1.926}{118.1} }\) After solving the fractions: x ≈ 2 So, the value of x is approximately 2, which means that 2 moles of NaOH react with 1 mole of succinic acid in the given reaction.

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Most popular questions from this chapter

Potassium nitrate decomposes upon heating to form potassium oxide, nitrogen gas, and oxygen gas. If \(19.6 \mathrm{~g}\) of potassium nitrate have decomposed, how many molecules of oxygen gas have been formed?

A compound used as an insecticide that contains only \(C, H\), and \(C l\) is subjected to combustion analysis, yielding \(24.78 \% \mathrm{C}\) and \(2.08 \% \mathrm{H}\). (a) What is the empirical formula for this compound? (b) What is the molecular formula if its actual formula is four times the mass of its empirical formula?

Consider the following unbalanced chemical equation: \(\mathrm{H}_{2}+\mathrm{N}_{2} \rightarrow \mathrm{NH}_{3}\) (a) To run this reaction in a balanced fashion, how much nitrogen is required if you start with \(10.0 \mathrm{~g}\) of \(\mathrm{H}_{2} ?\) (b) How many grams of ammonia \(\left(\mathrm{NH}_{3}\right)\) will you produce if you run the reaction with the masses calculated in part (a)? (c) How many molecules of ammonia will you produce?

A \(1.000-\mathrm{g}\) sample of a liquid is subjected to combustion analysis, yielding \(92.3 \% \mathrm{C}\) and \(7.7 \% \mathrm{H}\). It may or may not also contain oxygen. (a) What is the empirical formula for this compound? (b) The molar mass of this compound is determined to be about \(78 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula for this compound?

What is the empirical formula of a compound that is \(17.552 \% \mathrm{Na}, 39.696 \% \mathrm{Cr}\), and \(42.752 \% \mathrm{O} ?\)
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