Introduction:

In order to determine the fraction of the total pressure exerted by hydrogen when equal masses of ethane and hydrogen are mixed in an empty container at 25°C, we need to consider the ideal gas law and Dalton's law of partial pressures.

1. The Ideal Gas Law:

The ideal gas law states that the pressure (P) of a gas is directly proportional to its temperature (T) and the number of moles (n) of gas present, while inversely proportional to the volume (V) it occupies. The equation for the ideal gas law is given by:

PV = nRT

Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature

2. Dalton's Law of Partial Pressures:

Dalton's law of partial pressures states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas. Mathematically, it can be expressed as:

P_total = P_1 + P_2 + P_3 + ...

Where:
P_total = Total pressure
P_1, P_2, P_3, ... = Partial pressures of each gas component

3. Calculation:

In the given scenario, equal masses of ethane and hydrogen are mixed in an empty container at 25°C. Since the masses are equal, it implies that the number of moles of ethane and hydrogen will also be equal.

3.1. Step 1: Calculate the partial pressure of ethane:

Since the masses are equal, the number of moles of ethane and hydrogen will be the same. Thus, the partial pressure of ethane can be calculated using the ideal gas law equation:

PV = nRT

Rearranging the equation to solve for the partial pressure (P), we have:

P_ethane = n_ethane * (RT / V)

3.2. Step 2: Calculate the partial pressure of hydrogen:

Since the masses of ethane and hydrogen are equal, the number of moles of hydrogen will also be the same as the number of moles of ethane. Therefore, the partial pressure of hydrogen can be calculated using the same equation as in Step 1:

P_hydrogen = n_hydrogen * (RT / V)

3.3. Step 3: Calculate the total pressure:

According to Dalton's law of partial pressures, the total pressure exerted by the mixture is the sum of the partial pressures of each gas component. In this case, the total pressure is given by:

P_total = P_ethane + P_hydrogen

3.4. Step 4: Calculate the fraction of the total pressure exerted by hydrogen:

The fraction of the total pressure exerted by hydrogen can be calculated by dividing the partial pressure of hydrogen by the total pressure:

Fraction of pressure exerted by hydrogen = P_hydrogen / P_total

Summary:

To determine the fraction of the total pressure exerted by hydrogen when equal masses of ethane and hydrogen are mixed in an empty container at 25°C, we use the ideal gas law and Dalton's law of partial pressures. By calculating the partial pressure of each gas component and then finding the total pressure