Question

Write a chemical equation to represent the complete combustion of malonic acid, a compound with \(34.62 \% \mathrm{C}, 3.88 \% \mathrm{H},\) and \(61.50 \% \mathrm{O},\) by mass.

Short answer

The balanced chemical equation that represents the complete combustion of malonic acid is: \(4C_2H_2O + 5O_2 \rightarrow 8CO_2 + 2H_2O\)

Step-by-step solution

Calculate Empirical Formula

Assume a 100 g sample, so the percentages become grams. Then, divide these values by the molar mass of each element to find the number of moles for each element. Calculate ratio of moles of each element in the compound: - No. of moles of Carbon \(C\) = 34.62 g / 12.01 g/mol = 2.88 mol - No. of moles of Hydrogen \(H\) = 3.88 g / 1.008 g/mol = 3.85 mol - No. of moles of Oxygen \(O\) = 61.50 g / 16 g/mol = 3.84 mol Then, divide each of the calculated moles by the smallest value, which in this case is 3.84. - \(C = 2.88/3.84 =0.75 = 2 (approx.)\) - \(H = 3.85/3.84 = 1 (approx.)\) - \(O = 3.84/3.84 = 1 (approx.)\) This gives us the empirical formula as \(C_2H_2O\)

Write the Combustion Reaction

The next step is to write the full combustion reaction using the empirical formula calculated. Complete combustion involves the reaction of a substance with oxygen to produce carbon dioxide and water. The chemical equation is:\(C_2H_2O+ O_2 \rightarrow CO_2 + H_2O\)

Balance the Equation

To complete this problem, balance the equation by making sure that the number of atoms for every element is equal on both sides. The balanced equation becomes: \(4C_2H_2O + 5O_2 \rightarrow 8CO_2 + 2H_2O\)

Key concepts

Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements within it. To determine the empirical formula of a compound such as malonic acid, the first step is to convert the percentage composition of each element to grams. This is typically done by assuming a 100-gram sample of the substance.

• For Carbon (C), we have 34.62 grams.
• For Hydrogen (H), it is 3.88 grams.
• For Oxygen (O), it is 61.50 grams.

To find the number of moles of each element in the compound, divide the mass of each element by its respective molar mass (found on the periodic table).
The next step involves comparing the moles of each element by dividing by the smallest number of moles calculated. This produces a ratio that often needs rounding to the nearest whole number, unless it is very close to a simple fraction.
In this exercise, we find that the empirical formula for malonic acid is \(C_2H_2O\). This means in its simplest ratio, for every 2 carbon atoms, there are 2 hydrogen atoms and 1 oxygen atom.

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction. It shows the reactants transforming into the products, often involving changes in the bonds between atoms.
Writing a chemical equation starts with knowing the empirical formula of the reactant and the known products. In the complete combustion of compounds that contain carbon (C), hydrogen (H), and oxygen (O), the usual products are carbon dioxide \(CO_2\) and water \(H_2O\).To represent a combustion reaction, the formula of the substance being combusted is written on the left side, while the products, \(CO_2\) and \(H_2O\), are written on the right.
For example, the empirical formula \(C_2H_2O\) combusts in oxygen \(O_2\) as follows:

• \(C_2H_2O + O_2 \rightarrow CO_2 + H_2O\)

This equation expresses the basic idea that malonic acid reacts with oxygen to produce carbon dioxide and water.

Balancing Equations

Balancing a chemical equation is an essential step in completing a chemical reaction description. This ensures the law of conservation of mass is followed, stating that matter can neither be created nor destroyed.
The goal is to have the same number of each type of atom on both sides of the equation. Balancing is typically done by adjusting the coefficients (the numbers before molecules) in the equation—not by changing the chemical formulas of the compounds.In the combustion reaction of malonic acid, after writing the initial equation, the process involves counting the number of each type of atom on both sides and making them equal. Starting with the empirical formula \(C_2H_2O\), the balanced chemical equation becomes:

• \(4C_2H_2O + 5O_2 \rightarrow 8CO_2 + 2H_2O\)

This is achieved by making sure that the number of carbon, hydrogen, and oxygen atoms are the same in the reactants and products.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses the balanced chemical equation to determine the relative amounts of each substance involved.
Through stoichiometry, one can predict the quantities of products that will form in a reaction based on the amounts of reactants used, or vice versa.To engage in stoichiometric calculations:

• Start with a balanced equation, like the one derived from malonic acid \(4C_2H_2O + 5O_2 \rightarrow 8CO_2 + 2H_2O\).
• Use the coefficients in the equation to construct mole ratios.
• Utilize these ratios to calculate the mass or volume of other reactants or products.

This means if you start with a certain amount of \(C_2H_2O\), you can calculate how much \(O_2\) is needed and how much \(CO_2\) and \(H_2O\) are produced. This is key in fields from environmental science to industrial chemistry.