Question

The gaseous hydrocarbon acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) is used in welders' torches because of the large amount of heat released when acetylene burns with oxygen. $$ 2 \mathrm{C}_{2} \mathrm{H}_{2}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ How many grams of oxygen gas are needed for the complete combustion of \(150 \mathrm{~g}\) of acetylene?

Short answer

To completely combust 150 g of acetylene, 460.8 g of oxygen gas are needed.

Step-by-step solution

Calculate the moles of acetylene

Using the given mass of acetylene (150 g) and its molar mass (26.04 g/mol), we can calculate the number of moles of acetylene: $$ \text{moles of acetylene} = \frac{\text{mass of acetylene}}{\text{molar mass of acetylene}} = \frac{150 \mathrm{~g}}{26.04 \mathrm{~g/mol}} = 5.76 \mathrm{~mol} $$

Use the stoichiometry from the balanced equation to find the moles of oxygen gas

We can use the balanced equation to determine the ratio between moles of acetylene and moles of oxygen gas: $$ 2 \mathrm{mol~C_2H_2}:5 \mathrm{mol~O_2} $$ From this, we can determine the moles of oxygen gas required for the complete combustion of 5.76 moles of acetylene: $$ \text{moles of oxygen gas} = \frac{5.76 \mathrm{~mol} \ \mathrm{C}_{2} \mathrm{H}_{2} \times 5 \mathrm{~mol} \ \mathrm{O}_{2}}{2 \mathrm{~mol} \ \mathrm{C}_{2} \mathrm{H}_{2}} = 14.4 \mathrm{~mol} \ \mathrm{O}_{2} $$

Calculate the mass of oxygen gas required

Finally, we can convert the moles of oxygen gas to grams using its molar mass (32.00 g/mol): $$ \text{mass of oxygen gas} = \text{moles of oxygen gas} \times \text{molar mass of oxygen gas} = 14.4 \mathrm{~mol} \ \mathrm{O}_{2} \times 32.00 \mathrm{~g/mol} \ \mathrm{O}_{2} = 460.8 \mathrm{~g} $$ To completely combust 150 g of acetylene, 460.8 g of oxygen gas are needed.

Key concepts

Chemical Reaction

When we talk about a chemical reaction, we are referring to the process by which substances, known as reactants, transform into new substances called products. This transformation happens through the breaking and forming of chemical bonds, leading to a change in the composition of the involved substances. In the context of our exercise, the chemical reaction is the combustion of acetylene (\( \text{C}_2\text{H}_2 \)) when it reacts with oxygen (\( \text{O}_2 \)) to form carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2\text{O} \)).

Understanding a chemical reaction involves knowing the reactants and products, their states of matter, and how they interact according to the Law of Conservation of Mass, which states that mass is neither created nor destroyed in a chemical reaction. Therefore, what is present at the start must equal what results at the end, albeit rearranged into new substances.

Molar Mass

The molar mass of a substance is the weight of one mole (\(6.022 \times 10^{23}\) particles) of that substance expressed in grams per mole (g/mol). It is the sum of the atomic masses of all atoms in the molecule. For instance, in our exercise, acetylene has a molar mass of 26.04 g/mol, which is calculated by adding twice the atomic mass of carbon (approximately 12.01 g/mol each) to twice the atomic mass of hydrogen (approximately 1.008 g/mol each).

Understanding the concept of molar mass is integral to stoichiometry as it allows us to convert between mass in grams and amount in moles, facilitating quantitative analysis of substances involved in a chemical reaction.

Balanced Chemical Equation

A balanced chemical equation provides a macroscopic quantitative representation of a chemical reaction. It shows the number of units (usually moles) of each substance involved. To be balanced, the number of atoms for each element must be the same on both sides of the equation, complying with the Law of Conservation of Mass. In the example provided, the balanced equation is \(2 \text{C}_2\text{H}_2(g) + 5 \text{O}_2(g) \rightarrow 4 \text{CO}_2(g) + 2 \text{H}_2\text{O}(g)\).

Understanding how to balance chemical equations is essential because it allows us to predict the amounts of products formed and reactants needed. In stoichiometry, this skill is used to calculate mole relationships, which in turn help determine the mass of reactants consumed and products formed.

Combustion Reaction

A combustion reaction is a specific type of chemical reaction where a substance combines with oxygen to release energy in the form of light or heat. This reaction often involves hydrocarbons (compounds composed of hydrogen and carbon) and always results in the production of carbon dioxide and water as products, as long as sufficient oxygen is supplied and complete combustion occurs.

In the exercise, acetylene burns in a combustion reaction. The heat released in this reaction is harnessed in applications such as welding. Here, stoichiometry allows us to calculate the exact amount of oxygen needed to ensure complete combustion, thus avoiding the production of unwanted byproducts, such as carbon monoxide, which can occur if the oxygen supply is insufficient.