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Chapter 11: Problem 85

Consider two identical \(1-\mathrm{L}\) containers, both at room temperature \((300 \mathrm{~K})\). One of them contains 1 mole of helium gas, and the other contains 1 mole of hydrogen gas. Is the pressure higher in the helium container, higher in the hydrogen container, or the same in the two containers?

Short Answer

Expert verified
The pressures in both the helium and hydrogen containers are the same, as per the Ideal Gas Law \(PV = nRT\), because they have equal volume (1 L), equal number of moles (1 mole), and equal temperature (300 K). The formula results in equal pressure values for both containers: \(P_{He} = P_{H2} = \frac{1mol \times R \times 300K}{1L}\).

Step by step solution

01

Ideal Gas Law Formula

First, we need to understand the Ideal Gas Law formula: \(PV = nRT\) where: - P is the gas pressure, - V is the gas volume, - n is the number of moles of the gas, - R is the ideal gas constant, and - T is the gas temperature in Kelvin.
02

Compare the Gases

In our case, we have the following information for both helium and hydrogen gases: - V (volume) = 1 L - n (number of moles) = 1 mole - T (temperature) = 300 K And the ideal gas constant, R, is the same for all ideal gases. So, our comparison should be based only on the pressure (P), as all other values are equal.
03

Plug Values into the Formula

For helium gas (He): \(P_{He} \times 1L = 1mol \times R \times 300K\) \(P_{He} = \frac{1mol \times R \times 300K}{1L}\) For hydrogen gas (H₂): \(P_{H2} \times 1L = 1mol \times R \times 300K\) \(P_{H2} = \frac{1mol \times R \times 300K}{1L}\)
04

Compare Pressures

Now let's compare the pressures: \(P_{He} = P_{H2} = \frac{1mol \times R \times 300K}{1L}\) Since both pressures are equal, we can conclude that: Pressures in both helium and hydrogen containers are the same.

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Most popular questions from this chapter

Which variable is not needed to describe the behavior of an ideal gas: volume, number of moles, temperature, molar mass, or pressure?

A 7.24-g sample of gas is contained in a 4.00-L flask. Its pressure is \(765.0 \mathrm{~mm} \mathrm{Hg}\), and its temperature is \(25.0^{\circ} \mathrm{C}\). What is the molar mass of this gas?

According to the ideal gas law: (a) If you measured \(P, V, n\), and \(T\) for any gas sample and then calculated the quantity \(P V / n T\), what would be the units and numerical value of the result? (b) If you measured \(P, V, n\), and \(T\) for any gas sample and then calculated \(P V / n R T\), what would be the units and numerical value of the result?

A sample of hydrogen gas, \(\mathrm{H}_{2}\), is in an outdoor 1000.0-gallon tank. It is winter, and the temperature is \(-4.50^{\circ} \mathrm{C}\). A pressure gauge indicates that the pressure inside the tank is \(32.6\) atm. How many pounds of hydrogen are left in the tank? (Hint: Examine the solution to Problem 11.9.)

To what temperature must a gas initially at \(20.0^{\circ} \mathrm{C}\) be heated to double the volume and triple the pressure?
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