Chlorine gas was first prepared in 1774 by the oxidation of NaCl with MnO2 : 2 NaCl(s)+2 H2 SO4

step 1 Gives us a gas, some gas products. So it gives us a reaction of sodium chloride to form chlorine

Chlorine gas was first prepared in 1774 by the oxidation of...

Chlorine gas was first prepared in 1774 by the oxidation of $\mathrm{NaCl}$ with $\mathrm{MnO}_{2} :$ $$ \begin{aligned} 2 \mathrm{NaCl}(s)+2 \mathrm{H}_{2} \mathrm{SO}_{4}(l)+\mathrm{MnO}_{2}(s) \\ \mathrm{Na}_{2} \mathrm{SO}_{4}(s)+\mathrm{MnSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2}(g) \end{aligned} $$ Assume that the gas produced is saturated with water vapor at a partial pressure of 28.7 $\mathrm{mm}$ Hg and that it has a volume of 0.597 $\mathrm{L}$ at $27^{\circ} \mathrm{C}$ and 755 $\mathrm{mm}$ Hg pressure. (a) What is the mole fraction of $\mathrm{Cl}_{2}$ in the gas? (b) How many grams of NaCl were used in the experiment, assuming complete reaction?

Chlorine gas was first prepared in 1774 by the oxidation of $\mathrm{NaCl}$ with $\mathrm{MnO}_{2} :$
$$
\begin{aligned} 2 \mathrm{NaCl}(s)+2 \mathrm{H}_{2} \mathrm{SO}_{4}(l)+\mathrm{MnO}_{2}(s) \\ \mathrm{Na}_{2} \mathrm{SO}_{4}(s)+\mathrm{MnSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2}(g) \end{aligned}
$$
Assume that the gas produced is saturated with water vapor at a partial pressure of 28.7 $\mathrm{mm}$ Hg and that it has a volume of 0.597 $\mathrm{L}$ at $27^{\circ} \mathrm{C}$ and 755 $\mathrm{mm}$ Hg pressure.
(a) What is the mole fraction of $\mathrm{Cl}_{2}$ in the gas?
(b) How many grams of NaCl were used in the experiment, assuming complete reaction?

Key Concepts

Stoichiometry

Stoichiometry involves using the balanced chemical equation to relate the amounts of reactants and products. It provides the quantitative relationships between reactants consumed and products formed, which is essential when calculating the mass of a specific reactant or product based on gas volume and mole calculations.

Saturated Vapor Pressure

Saturated vapor pressure is the equilibrium pressure established by a vapor when it is in contact with its liquid phase at a given temperature. In problems involving gas mixtures, knowing the saturated vapor pressure is important because it represents the maximum partial pressure of that vapor in the mixture, affecting overall gas composition calculations.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, number of moles, and temperature of a gas. It is a fundamental tool in chemistry for converting between these variables, especially when determining the quantity of gas present in a reaction or a given system under non-extreme conditions.

Mole Fraction

The mole fraction is the ratio of the number of moles of one component to the total number of moles in a mixture. It serves as a way to represent the composition of gas mixtures and is directly related to partial pressures in ideal gas systems, making it a critical concept in understanding how individual gas contributions compare to the whole.

Partial Pressure

Partial pressure is the pressure that an individual gas in a mixture would exert if it alone occupied the entire volume at the same temperature. Dalton’s law of partial pressures states that the total pressure of a gas mixture is equal to the sum of the individual partial pressures, and this principle is essential when dealing with gas mixtures containing water vapor or other condensable components.

Transcript

00:02 Gives us a gas, some gas products.

00:04 So it gives us a reaction of sodium chloride to form chlorine gas and water vapor.

00:08 It tells us that the partial pressure of water vapor is 28 .7 millimeters of mercury.

00:13 And the volume of the chlorine gas, this is important, this is all for chlorine gas specifically, is 0 .597 liters, the temperature is 27 degrees celsius, and the total pressure of both gases is 750.

00:30 155 millimeters of mercury.

00:33 So first, we need to find the molar fraction of chlorine gas, and then we need to see what was the original amount of grams of sodium chloride in the beginning of the reaction.

00:44 So first to find the molar fraction, we need to find the partial pressure of chlorine gas.

00:49 So to do that, we're going to subtract the total pressure from the partial pressure of h2o, because total pressure is equal to the partial pressure of h2o, plus the partial pressure of chlorine gas.

01:04 So if we subtract 28 .7 from 755, we get 726 millimeters of mercury.

01:18 So a partial pressure is equal to the molar fraction times the total pressure.

01:26 So to find the molar fraction, we're just going to divide 726 by 755 and then we're left with 0 .96 as our molar fraction.

01:48 So now we need to see what was the amount of sodium chloride in the beginning.

01:53 So first we need to find the total number or the number of moles of chlorine gas so specific to chlorine gas.

02:01 So to do that we'll do and equals we'll use the ideal gas law.

02:05 So n equals pv divided by r t so for pressure we need to use the partial pressure of chlorine gas because we need to know the moles of chlorine gas.

02:18 So converting 726 to divided by 760 to get atm.

02:25 We're left with 0 .955 atm...

Please give Ace some feedback