Question

Which of the following correctly balances the chemical equation given below? There may be more than one correct balanced equation. If a balanced equation is incorrect, explain why it is incorrect. $$\mathrm{CaO}+\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}$$ a. \(\mathrm{CaO}_{2}+3 \mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}\) b. \(2 \mathrm{CaO}+5 \mathrm{C} \rightarrow 2 \mathrm{CaC}_{2}+\mathrm{CO}_{2}\) c. \(\mathrm{CaO}+2 ^{1/2} \mathrm{C} \rightarrow \mathrm{CaC}_{2}+1 / 2 \mathrm{CO}_{2}\)d. \(4 \mathrm{CaO}+10 \mathrm{C} \rightarrow 4 \mathrm{CaC}_{2}+2 \mathrm{CO}_{2}\)

Short answer

The correct balanced equation from the given options is d. \(4 \mathrm{CaO}+10 \mathrm{C} \rightarrow 4\mathrm{CaC}_{2}+2 \mathrm{CO}_{2}\), which simplifies to \(\mathrm{CaO}+2\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}\).

Step-by-step solution

Balancing the given chemical equation

Let's first accomplish this ourselves by balancing the given chemical equation: $$\mathrm{CaO}+\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}$$ First, observe the number of atoms per element both before (left side) and after (right side) the equation: - Left: 1 calcium (Ca), 1 oxygen (O), and 1 carbon (C) - Right: 1 calcium (Ca), 2 carbons (C*_2*), 1 carbon (C), 2 oxygen (O*_2*) Now, let's balance the carbons first by placing a 2 in front of the C on the left side. So we have: $$\mathrm{CaO}+2\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}$$ The equation is balanced now as the number of each element's atoms is the same on both sides.

Check the given options for correctness

Now let's check whether each given balanced equation option is correct or not: a. \(\mathrm{CaO}_{2}+3 \mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}\) - This option is incorrect because it wrongly adds an extra oxygen to the left side. b. \(2 \mathrm{CaO}+5 \mathrm{C} \rightarrow 2\mathrm{CaC}_{2}+\mathrm{CO}_{2}\) - This option is incorrect because it multiplies the left side by 2 while adding an extra carbon to the right side. This doesn't balance the given equation. c. \(\mathrm{CaO}+2 ^{1/2} \mathrm{C} \rightarrow \mathrm{CaC}_{2}+1 / 2\mathrm{CO}_{2}\) - This option is incorrect because it uses fractional coefficients which violate the rules of balancing chemical equations. d. \(4 \mathrm{CaO}+10 \mathrm{C} \rightarrow 4\mathrm{CaC}_{2}+2 \mathrm{CO}_{2}\) - This option is correct. Although not written with the smallest possible coefficients, it's still balanced. By dividing both sides by 2, we get the balanced equation we found earlier: $$\mathrm{CaO}+2\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}$$ So, from the given options, option d. is the only correct balanced equation.

Key concepts

Chemical Reactions

A chemical reaction is a process where reactants transform into products through the breaking and forming of chemical bonds. Understanding chemical equations is critical because they depict the transformation. The equation $$\mathrm{CaO}+\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2}$$ represents such a chemical transformation, where calcium oxide reacts with carbon to produce calcium carbide and carbon dioxide. Each substance in this equation is represented by a chemical formula that denotes the number of atoms for each element involved.

For instance, \(\mathrm{CaO}\) shows that one molecule of calcium oxide contains one calcium atom and one oxygen atom. Similarly, \(\mathrm{CaC}_{2}\) illustrates that one molecule of calcium carbide contains one calcium atom and two carbon atoms. The products and reactants listed in this equation are the core pieces that we use to understand the conservation of mass, stoichiometry, and the specific proportions necessary to balance a chemical equation.

Stoichiometry

Stoichiometry refers to the calculation of reactants and products in chemical reactions and is a fundamental concept in chemistry that ensures the laws of conservation of mass and definite proportions are upheld. The stoichiometry of a chemical reaction can be understood through the balanced chemical equation, which provides the molar relationship between the reactants and products.

For example, in the reaction $$\mathrm{CaO}+2\mathrm{C} \rightarrow \mathrm{CaC}_{2}+\mathrm{CO}_{2},$$ each mole of calcium oxide reacts with two moles of carbon to produce one mole of calcium carbide and one mole of carbon dioxide. This stoichiometric ratio is vital for calculations such as determining the amount of reactants needed to produce a desired quantity of products, or calculating the yield of a reaction.

Conservation of Mass

The conservation of mass is a fundamental principle in chemistry stating that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. According to this law, the mass of the reactants must equal the mass of the products.

When balancing chemical equations, we ensure that the number of atoms for each element is the same on both sides of the equation, reflecting this conservation. Taking our example, the initial unbalanced equation shows mismatched numbers of atoms. Upon balancing, we demonstrate that two carbon atoms on both sides, one calcium atom, and two oxygen atoms are present, showing that mass is conserved. This principle guides us in making sure our chemical equations reflect reality, where matter is not lost, just rearranged.