Question

Calcium carbide, \(\mathrm{CaC}_{2}\), reacts with water to produce acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}\) $$ \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{Ca}(\mathrm{OH})_{2}(s) $$ What volume of acetylene at 25 ' \(\mathrm{C}\) and 1.01 atm is generated by the complete reaction of \(2.49 \mathrm{~g}\) of calcium carbide? What volume would this quantity of acetylene occupy at STP?

Short answer

The volume of acetylene generated by the complete reaction of 2.49 g of calcium carbide at 25°C and 1.01 atm is 0.97 L. At STP (0°C and 1 atm), this quantity of acetylene would occupy a volume of 1.03 L.

Step-by-step solution

Calculate moles of calcium carbide

Since we are given the mass of calcium carbide and we know its molar mass, we can calculate the moles of calcium carbide that react with water. Calcium carbide, CaC₂, has a molar mass of: M(CaC₂) = M(Ca) + 2×M(C) = 40.08 g/mol + 2×12.01 g/mol = 64.10 g/mol. Using the given mass (2.49 g) and the molar mass (64.10 g/mol), we can find the moles of calcium carbide: moles(CaC₂) = mass(CaC₂) ÷ M(CaC₂) = 2.49 g ÷ 64.10 g/mol = 0.0388 mol.

Find moles of acetylene produced

Using the balanced chemical equation, we can determine the stoichiometric ratio between the moles of calcium carbide and acetylene produced: CaC₂ + 2 H₂O → C₂H₂ + Ca(OH)₂ The stoichiometric ratio between CaC₂ and C₂H₂ is 1:1. Therefore, the moles of acetylene produced equals the moles of calcium carbide reacted: moles(C₂H₂) = moles(CaC₂) = 0.0388 mol.

Find volume of acetylene at given conditions

We'll use the ideal gas law to find the volume of acetylene at the given conditions (25°C and 1.01 atm): PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant, and T is temperature in Kelvin. First, we need to convert 25°C to Kelvin: T = 25 + 273.15 = 298.15 K. R = 0.0821 L⋅atm/mol⋅K (Ideal Gas Constant) Now, we can solve for volume (V) of acetylene: V = nRT / P V = (0.0388 mol)(0.0821 L⋅atm/mol⋅K)(298.15 K) / 1.01 atm V = 0.97 L The volume of acetylene at 25°C and 1.01 atm is 0.97 L.

Find volume of acetylene at STP

STP conditions are 0°C and 1 atm. We can use the same ideal gas law to find the volume of acetylene at STP. First, we need to convert 0°C to Kelvin: T = 0 + 273.15 = 273.15 K. Now, we can solve for the volume (V) of acetylene at STP: V = nRT / P V = (0.0388 mol)(0.0821 L⋅atm/mol⋅K)(273.15 K) / 1 atm V = 1.03 L The volume of acetylene at STP is 1.03 L.

Key concepts

Stoichiometry

In chemistry, stoichiometry is crucial for understanding chemical reactions. It allows you to calculate the amounts of reactants and products involved in a chemical reaction.
Stoichiometry is based on the balanced chemical equation, which provides a direct relationship between the quantities of the reactants and the products formed. For instance, in the reaction of calcium carbide (\(\mathrm{CaC_2}\)) with water, the balanced equation is:

• \(\mathrm{CaC_2 + 2 \, H_2O \rightarrow C_2H_2 + Ca(OH)_2}\)

From this equation, we see that one mole of \(\mathrm{CaC_2}\) produces one mole of acetylene (\(\mathrm{C_2H_2}\)).
This 1:1 stoichiometric ratio is essential in predicting how much product can be formed from a given quantity of reactant. Knowing these ratios helps you convert mass to moles and vice versa, which is extremely useful in calculations.
So, stoichiometry is a key tool for predicting the outcomes of chemical reactions and is fundamental in fields ranging from pharmaceuticals to environmental science.

Ideal Gas Law

The ideal gas law is an equation of state for gases, combining several fundamental physical constants and describing how gases behave under various conditions. The formula is:\(PV = nRT\)
Where:

• \(P\) is pressure in atmospheres (atm)
• \(V\) is volume in liters (L)
• \(n\) is the amount of substance in moles
• \(R\) is the ideal gas constant, often 0.0821 L⋅atm/mol⋅K
• \(T\) is temperature in Kelvin (K)

The ideal gas law allows you to calculate any one of these variables if you know the other three. This equation is particularly useful in determining the volume of acetylene gas produced in our example reaction at non-standard conditions, such as 25°C and 1.01 atm.
By manipulating the ideal gas law, you can calculate how much space a certain amount of gas will occupy under different temperature and pressure conditions. It is a powerful utility for chemists and engineers alike.

Moles Calculation

Understanding moles is essential for any stoichiometric calculation. The mole is a fundamental unit in chemistry that quantifies chemical substances. One mole of any substance contains Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\) particles.
To calculate the number of moles, you need to know the mass of the substance and its molar mass. The formula is:\(\text{moles} = \frac{\text{mass}}{\text{molecular weight}}\).
For instance, in our scenario, we calculate the moles of calcium carbide (\(\mathrm{CaC_2}\)) by dividing its given mass (2.49 g) by its molar mass (64.10 g/mol), resulting in 0.0388 mol.
This calculation is pivotal as it sets the stage for all subsequent stoichiometric calculations, allowing us to assess how much product will be formed in the reaction.
Moles serve as the bridge between the mass of a substance and the number of atoms, molecules, or ions it contains, making it a cornerstone concept in chemistry.