Two flasks of equal volume and at the same temperature contain different gases. One flask contains 5.0 g of O 2 and the other flask contains 5.0 g of H 2 . Is each of the following statements true or false ? Explain. b. The pressures in the flasks are the same.

Hey, everyone, we're asked to consider two tanks with identical volumes and both are at the same temperature. The first tank contains 3.5 g of fluorine gas, which has a formula of F two. While the second tank contains 3.5 g of chlorine gas, which has a formula of C L two, determine whether the following statement is true or false and justify your answer. And the statement is that the pressure in the first tank is greater than the pressure in the second tank. To answer this question, we need to recall our ideal gas equation which tells us that our pressure times our volume is equal to our moles times our gas constant times our temperature. Now another way to rewrite our mole is mass over the molar mass. Now let's go ahead and rewrite this equation using that information and isolating our pressure. So we have our pressure and this is going to be equal to our mass times our gas constant times our temperature divided by both our molar mass and our volume. Now in our question stem, they told us that both tanks had identical volumes. So our volume will be constant, our gas constant is also constant, the mass is constant as well and our temperature is also constant. So essentially, we want to focus on our molar mass. And through this equation, we can see that our pressure is inversely proportional to our molar mass. In other words, if our pressure is higher, our molar mass will be lower and vice versa. So if our pressure is lower, our molar mass will be higher. Now, let's go ahead and use this information to answer this question starting with our tank one, which is our fluorine gas. Now, when we look at our periodic table, we see that the molar mass of fluorine comes up to 19. g per mole. And we're going to multiply this by two of fluorine since we have two of fluorine in our chemical formula. When we calculate this out, we end up with 38.0 g per mole. Now let's go ahead and take a closer look at tank two, which is our chlorine gas. When we look at our periodic table, chlorine has a molar mass of 35. g per mole. And we're going to multiply this by two of chlorine. Since we have two of chlorine in our chemical formula, this gets us to a total of 70.9 g per mole. Based on our calculations, we can see that the molar mass of chlorine is less than the molar mass of chlorine. So this means that fluorine will have a higher pressure due to that inversely proportional relationship. So to answer this question, the pressure in the first tank is greater than the pressure in the second tank. Because the molar mass of fluorine is less than the molar mass of chlorine, which means there are more moles of gas present in the first tank than in the second tank. So our final answer here will be true. Now, I hope this made sense and let us know if you have any questions.

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8. Gases, Liquids and Solids

The Ideal Gas Law Applications

GOB Chemistry

8. Gases, Liquids and Solids

The Ideal Gas Law Applications

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Problem 64b

Textbook Question

Two flasks of equal volume and at the same temperature contain different gases. One flask contains 5.0 g of O₂ and the other flask contains 5.0 g of H₂. Is each of the following statements true or false? Explain.
b. The pressures in the flasks are the same.

Verified step by step guidance

Step 1: Recall the Ideal Gas Law, which is expressed as

PV = nRT

. Here, P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Since the flasks have the same volume (V) and are at the same temperature (T), the pressure (P) depends on the number of moles (n) of gas in each flask.

Step 2: Calculate the number of moles of O₂ in the first flask. Use the formula

n = rac{m}{M}

, where m is the mass of the gas and M is its molar mass. For O₂, the molar mass is approximately 32.00 g/mol. Substitute m = 5.0 g and M = 32.00 g/mol to find the moles of O₂.

Step 3: Calculate the number of moles of H₂ in the second flask using the same formula,

n = rac{m}{M}

. For H₂, the molar mass is approximately 2.016 g/mol. Substitute m = 5.0 g and M = 2.016 g/mol to find the moles of H₂.

Step 4: Compare the number of moles of O₂ and H₂. Since the pressure in each flask depends on the number of moles (n) and the number of moles is different for O₂ and H₂ due to their differing molar masses, the pressures in the flasks will not be the same.

Step 5: Conclude that the statement 'The pressures in the flasks are the same' is false, and explain that the difference arises because the number of moles of gas in each flask is different, even though the masses of the gases are the same.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law helps in understanding how gases behave under different conditions and is essential for analyzing the scenario presented in the question.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Different gases have different molar masses, which affects their behavior in a given volume and temperature. In the context of the question, the molar masses of O₂ and H₂ are crucial for determining the number of moles present in each flask, which directly influences the pressure exerted by each gas.

Gas Pressure

Gas pressure is the force exerted by gas molecules colliding with the walls of their container. According to the Ideal Gas Law, if the volume and temperature are constant, the pressure of a gas is directly proportional to the number of moles of gas present. Therefore, to determine if the pressures in the two flasks are the same, one must compare the number of moles of O₂ and H₂ based on their respective masses and molar masses.

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