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.

Question

b. The pressures in the flasks are the same.

Accepted Answer

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.

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 video answer for a similar problem:

Key Concepts

Ideal Gas Law

Molar Mass

Gas Pressure