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A sample of limestone (containing calcium carbonate, \(\mathrm{CaCO}_{3}\) ) weighing \(438 \mathrm{mg}\) is treated with oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) to give calcium oxalate, \(\mathrm{CaC}_{2} \mathrm{O}_{4}\) $$ \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \longrightarrow \mathrm{CaC}_{2} \mathrm{O}_{4}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g) $$ The mass of the calcium oxalate produced is \(469 \mathrm{mg}\). What is the mass percentage of calcium carbonate in this limestone?

Short Answer

Expert verified
The mass percentage of calcium carbonate in the limestone is 83.56%.

Step by step solution

01

Find the Molar Mass of Calcium Carbonate

The molar mass of calcium carbonate, \( \text{CaCO}_3 \), is calculated by summing the atomic masses: \( \text{Ca} = 40.08 \text{g/mol} \), \( \text{C} = 12.01 \text{g/mol} \), and \( \text{O} = 16.00 \text{g/mol} \times 3 \). Therefore, the molar mass of \( \text{CaCO}_3 \) is \( 40.08 + 12.01 + 48.00 = 100.09 \text{g/mol} \).
02

Find the Molar Mass of Calcium Oxalate

The molar mass of calcium oxalate, \( \text{CaC}_2\text{O}_4 \), is calculated by summing the atomic masses: \( \text{Ca} = 40.08 \text{g/mol} \), \( \text{C} = 12.01 \text{g/mol} \times 2 \), and \( \text{O} = 16.00 \text{g/mol} \times 4 \). Therefore, the molar mass of \( \text{CaC}_2\text{O}_4 \) is \( 40.08 + 24.02 + 64.00 = 128.10 \text{g/mol} \).
03

Convert Mass of Calcium Oxalate to Moles

The mass of calcium oxalate produced is \( 469 \text{ mg} = 0.469 \text{ g} \). The moles of \( \text{CaC}_2\text{O}_4 \) are \( \frac{0.469 \text{ g}}{128.10 \text{ g/mol}} = 0.00366 \text{ moles} \).
04

Use Stoichiometry to Find Moles of Calcium Carbonate

The reaction shows that \( 1 \text{ mole} \) of \( \text{CaCO}_3 \) gives \( 1 \text{ mole} \) of \( \text{CaC}_2\text{O}_4 \). Hence, the moles of \( \text{CaCO}_3 \) are the same as the moles of \( \text{CaC}_2\text{O}_4 \), which is \( 0.00366 \text{ moles} \).
05

Convert Moles of Calcium Carbonate to Mass

The mass of \( \text{CaCO}_3 \) is \( 0.00366 \text{ moles} \times 100.09 \text{ g/mol} = 0.366 \text{ g} = 366 \text{ mg} \).
06

Calculate Mass Percentage of Calcium Carbonate

The mass percentage of calcium carbonate in the limestone is \( \left( \frac{366 \text{ mg}}{438 \text{ mg}} \right) \times 100\% = 83.56\% \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass Calculation
Understanding molar mass is key to solving many chemical problems. The molar mass of a compound represents the mass of one mole of that substance and is expressed in grams per mole (\(\text{g/mol}\)). To find the molar mass, you need to sum the atomic masses of all the atoms present in the molecular formula. Let's take calcium carbonate (\(\text{CaCO}_3\)) as an example.
  • Calcium (\(\text{Ca}\)) contributes 40.08 \(\text{g/mol}\).
  • Carbon (\(\text{C}\)) contributes 12.01 \(\text{g/mol}\).
  • Oxygen (\(\text{O}\)) has a mass of 16.00 \(\text{g/mol}\), and since there are three oxygens, it contributes 48.00 \(\text{g/mol}\).
Summing these, the molar mass of \(\text{CaCO}_3\) is 100.09 \(\text{g/mol}\). Similar calculations are done for calcium oxalate (\(\text{CaC}_2\text{O}_4\)) by summing the masses of each atom contained in the formula.
This step is crucial as it allows conversion from mass to moles, which is a necessary step in calculating the reactants and products of a chemical equation.
Limestone Composition
To understand the composition of limestone, it is essential to know that it is primarily made up of calcium carbonate (\(\text{CaCO}_3\)). Limestone often serves a variety of purposes, from construction material to a component in industrial processes. In chemistry, determining the amount of calcium carbonate present in limestone helps calculate reactions involving limestone.
In our exercise, limestone's reaction with oxalic acid produces calcium oxalate (\(\text{CaC}_2\text{O}_4\)). By understanding the stoichiometry of this chemical reaction, we determine how much compound reacts and how much product we can expect. This process helps chemists identify the purity and percentage composition of limestone in sample analysis. In essence, knowing limestone's composition is key to calculating various chemical reactions and projections, ensuring that industries utilize it efficiently.
Mass Percentage Calculation
Mass percentage is a way to express concentration; it tells us what fraction of a sample's mass comes from a particular component. In our exercise, we wanted to find out what percentage of the limestone sample's mass is made up of calcium carbonate (\(\text{CaCO}_3\)).
Here's how to approach it:
  • First, calculate the mass of the component of interest (\(\text{CaCO}_3\) in our case).
  • Then, divide this mass by the total sample mass of the limestone and convert it to a percentage.
For our specific example, the mass of calcium carbonate calculated using stoichiometry was 366 mg. By dividing this by the total sample mass of 438 mg, and then multiplying the result by 100, we get the mass percentage: \(\left( \frac{366 \text{ mg}}{438 \text{ mg}} \right) \times 100\% \approx 83.56\% \).
Mass percentage provides crucial information on the purity and composition of substances in any kind of mixture or compound.

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Most popular questions from this chapter

Ethylene glycol is used as an automobile antifreeze and in the manufacture of polyester fibers. The name glycol stems from the sweet taste of this poisonous compound. Combustion of \(6.38 \mathrm{mg}\) of ethylene glycol gives \(9.06 \mathrm{mg}\) \(\mathrm{CO}_{2}\) and \(5.58 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .\) The compound contains only \(\mathrm{C}, \mathrm{H}\) and \(\mathrm{O}\). What are the mass percentages of the elements in ethylene glycol?

Acrylonitrile, \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N},\) is the starting material for the production of a kind of synthetic fiber (acrylics). It can be made from propylene, \(\mathrm{C}_{3} \mathrm{H}_{6},\) by reaction with nitric oxide, NO. \(4 \mathrm{C}_{3} \mathrm{H}_{6}(g)+6 \mathrm{NO}(g) \longrightarrow 4 \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g)\) How many grams of acrylonitrile are obtained from \(452 \mathrm{~kg}\) of propylene and excess \(\mathrm{NO} ?\)

Hew-many grams of \(\mathrm{NH}_{3}\) will have the same number of molecules as \(15.0 \mathrm{~g}\) of \(\mathrm{C}_{6} \mathrm{H}_{6} ?\) \(\begin{array}{ll}3.27 & 1.92\end{array}\) $$ 15.0 $$ \(17.0 \quad 14.2\)

A mixture consisting of \(11.9 \mathrm{~g}\) of calcium fluoride, \(\mathrm{CaF}_{2},\) and \(12.1 \mathrm{~g}\) of sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4},\) is heated to drive off hydrogen fluoride, HF. $$ \mathrm{CaF}_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(l) \longrightarrow 2 \mathrm{HF}(g)+\mathrm{CaSO}_{4}(s) $$ What is the maximum number of grams of hydrogen fluoride that can be obtained?

Potassium superoxide, \(\mathrm{KO}_{2}\), is employed in a selfcontained breathing apparatus used by emergency personnel as a source of oxygen. The reaction is $$ 4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g) $$ If a self-contained breathing apparatus is charged with \(750 \mathrm{~g}\) \(\mathrm{KO}_{2}\) and then is used to produce \(188 \mathrm{~g}\) of oxygen, was all of the \(\mathrm{KO}_{2}\) consumed in this reaction? If the \(\mathrm{KO}_{2}\) wasn't all consumed, how much is left over and what mass of additional \(\mathrm{O}_{2}\) could be produced?

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