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Question

# Calcium carbide reacts with water to produce acetylene gas according to the following equation:$\ce{CaC2 (s) + 2H2O (l) -> Ca(OH)2 (aq) + C2H2 (g)}$The product gas, $\ce{C2H2}$ is collected over water at a temperature of $25\degree\ce C$ and a pressure of $750\text{ mmHg}$. If the wet $\ce{C2H2}$ gas formed occupies a volume of $7.52\ce L$, the number of moles of $\ce{CaC2}$ reacted was _____ mol. The vapor pressure of water is $23.8\text{ mmHg}$ at $25\degree\ce C$.

Solution

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Two important concepts in chemistry are highlighted in this problem: Ideal Gas Law and Dalton's Law of Partial Pressure. The Ideal Gas Law defines the relationship of pressure, volume, temperature, and the number of gaseous moles in one formula as a combination of the four gas laws: Boyle's Law, Charles' Law, Gay-Lussac's Law, and Avogadro's Law. The formula is:

$PV=nRT$

where $P$ is the pressure, $V$ is the volume, $n$ is the mole of the gaseous molecule, $T$ is the absolute temperature, and $R$ is the ideal gas constant at $0.0821\text{ L atm/ mol K}$.

In addition to this, Dalton's Law of Partial Pressure is highlighted in the problem, which states that the partial pressure of gaseous molecule contributes to the sum total pressure experienced. The formula of Dalton's Law of Partial Pressure is:

$P_{total}=\sum P_i$

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