# Homework #4


## Q1

A mixture containing 0.538 mol He (g) and 0.103 mol Ar (g) is confined in a 7.00 L vessel at 25°C.

1. Calculate the partial pressure of each of the gases in the mixture
2. Calculate the total pressure

## Q2

A sample of 4.00 mL of diethylether ($$C_2H_5OC_2H_5$$, density = 0.7134 g/mL) is introduced into a 5.00 L vessel that already contains a mixture of $$N_2$$ and $$O_2$$, whose partial pressures are $$pN_2 = 0.715 \; atm$$ and $$pO_2 = 0.208\; atm$$. The temperature is held at 35.0 °C and the diethylether totally evaporates.

1. Calculate the partial pressure of the diethylether.
2. Calculate the total pressure of the container.

## Q3

A piece of sodium metal undergoes complete reaction with water as follows:

$2Na_{(s)} + 2H_2O_{(l)} \rightarrow 2NaOH_{(aq)} + H_{2\,(g)}$

The hydrogen gas is collected over water at $$25^oC$$. The volume of gas is 246 mL measured at 1 atm. Calculate the number of grams of $$Na$$ used in the reaction. (vapor pressure of water = 0.0313 atm)

## Q4

How many liters of ammonia gas is generated with 1 L of nitrogen gas reacts with 3 L of hydrogen gas via the following reaction (assuming no changing pressure and temperature):

$N_{2(g)} + 3H_{2(g)} \rightarrow 2NH_{3(g)}$

## Q5

Consider the combustion reaction of hydrogen (assuming no changing pressure and temperature)::

$2H_{2(g)} + O_{2(g)} \rightarrow 2H_2O_{(g)}$

1. What volume of steam is formed from 50 cm3 of hydrogen and 50 cm3 of oxygen mixed together?
2. What gas(s) is in excess and by how much?

## Q6

Consider two gases, $$A$$ and $$B$$, in separate 1.0 L containers at the same temperature and pressure. The total mass of gas $$A$$ in the container is 0.25 g and the mass of gas $$B$$ in the container is 0.51 g.

1. Which gas has the most molecules present?
2. Which gas has the largest average kinetic energy?
3. Which gas has the fastest average velocity?
4. How can the pressure in the two containers be equal to each other since the larger gas $$B$$ molecules collide with the container walls more forcefully?

## Q7

Calculate the root mean square speed for nitrogen gas at 217°C, helium gas at 27°C, and xenon gas at 27°C.

## Q8

The rate of effusion of a particular gas was measured to be 27.2 mL/min. Under the same conditions, the rate effusion of pure methane gas ($$CH_4$$) is 47.8 mL/min. What is the molar mass of the unknown gas? Hint: Use Graham's Law of Effusion.

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