What is the total pressure in atmospheres of a gas mixture that contains 1.0 g of H2 and 8.0 g o

What is the total pressure in atmospheres of a gas mixture...

Key Concepts

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is foundational for understanding how gas particles behave under different conditions. It relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas with the gas constant (R). This law is essential for problems involving gas mixtures because it allows one to calculate variables such as total pressure when the number of moles, volume, and temperature are known.

Mole Concept and Molar Mass Calculation

The mole concept is crucial in chemistry as it provides a bridge between the atomic/molecular scale and measurable quantities. Calculating the number of moles from a given mass, using the substance's molar mass, is a key step in determining how much gas is present. This calculation is necessary for applying the Ideal Gas Law to find pressures and other properties, particularly in gas mixture problems.

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure is the sum of the partial pressures exerted by each individual gas. Each gas contributes to the total pressure independently according to its number of moles, making it possible to compute the partial pressures once the overall conditions and composition of the mixture are known.

Transcript

00:01 In this question, we need to calculate the total pressure of a mix of different gases.

00:14 This mix contains one gram of hydrogen, eight grams of argon, and these two gases in the mix are contained in a three -liter tank or container.

00:41 The volume is 3 liters.

00:50 Because these are gases, we're going to use the formula of the ideal gas, which states that the product of the pressure and the volume equals the number of moles of the gas times the ideal gas constant times the temperature in gelding.

01:11 And that's an extra piece of information that we are giving.

01:14 We know that these gases are at a temperature of 27 degrees celsius.

01:24 We have to calculate the total pressure, and then we have to calculate the partial pressure of each of these two gases in the mix.

01:36 To calculate the partial pressure, to calculate the total pressure, we can do two ways.

01:43 We can calculate the total number of moles of gas in the mix by adding the moles of hydrogen plus the moles of argon or we can calculate which is a very long way we can calculate the partial pressure of each gas using the specific number of moles of each of the two gases and then that will give us the partial pressure and then add the pressure which means that we need to use the formula twice okay and that we will have to do more calculations.

02:21 So i prefer to calculate the total number of moles from the beginning, then calculate the total pressure, then calculate what is the percentage in terms of moles of each of the two gases, and that will give me the partial pressure when i multiply the ratio of one gas over the total by the total pressure.

02:51 So let's calculate the number of moles of each gas and the net total.

02:55 The number of mole of hydrogen is 1 gram divided by 2 grams per mole, which means 2 times 1 the atomic weight, 2 grams per mole.

03:14 And then i'm going to have 0 .5 moles.

03:19 Of hydrogen.

03:22 For argon, i have 8 grams of argon divided by 40 grams per mole, which is the atomic weight of argon.

03:44 And this will give me 8 divided by 40 is 0 .2 moles...

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