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Chapter 5: Problem 49

Suppose two 200.0-L tanks are to be filled separately with the gases helium and hydrogen. What mass of each gas is needed to produce a pressure of \(2.70 \mathrm{~atm}\) in its respective tank at \(24^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
To fill a 200.0-L tank with helium to 2.70 atm at 24°C, approximately 88.4 g of helium is needed. For a 200.0-L tank filled with hydrogen under the same conditions, approximately 44.2 g of hydrogen is required.

Step by step solution

01

Convert temperature to Kelvin

The temperature is given in Celsius (24°C), and we need to convert it to Kelvin. To do this, we simply add 273 to the Celsius value: \(T(K) = 24 + 273 = 297 K\)
02

Rearrange the ideal gas law formula for n (moles)

We need to find the number of moles of each gas needed to fill the tanks. So, let's rearrange the ideal gas law formula to solve for the number of moles (n): \(n = \frac{P \cdot V}{R \cdot T}\)
03

Calculate the moles of each gas required

Now, we can plug the values into the equation for helium: \(n_{He} = \frac{2.70\,\text{atm} \cdot 200.0\,\text{L}}{0.0821 \frac{L \cdot atm}{mol \cdot K} \cdot 297\,\text{K}} \approx 22.1\, \text{moles}\) And for hydrogen: \(n_{H2} = \frac{2.70\,\text{atm} \cdot 200.0\,\mathrm{L}}{0.0821 \frac{L \cdot atm}{mol \cdot K} \cdot 297\,\mathrm{K}} \approx 22.1\, \text{moles}\) The number of moles of each gas needed to fill their respective tanks to the desired pressure and temperature is approximately 22.1 moles.
04

Calculate the mass of each gas required

Finally, we'll use the molar mass (MM) of each gas to convert the number of moles needed (n) to mass (m). The mass (m) can be found with the following equation: \(m = n \cdot \mathrm{MM}\) For helium: \(m_{He} = 22.1\, \text{moles} \cdot 4.00\, \frac{\text{g}}{\mathrm{mol}} \approx 88.4\, \mathrm{g}\) For hydrogen: \(m_{H2} = 22.1\, \text{moles} \cdot 2.00\, \frac{\text{g}}{\mathrm{mol}} \approx 44.2\, \mathrm{g}\)
05

State the mass of each gas required to reach the desired conditions

The mass of helium needed to fill its tank to 2.70 atm at 24°C is approximately 88.4 g, and the mass of hydrogen needed to fill its tank to 2.70 atm at 24°C is approximately 44.2 g.

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Most popular questions from this chapter

Some very effective rocket fuels are composed of lightweight liquids. The fuel composed of dimethylhydrazine \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2} \mathrm{H}_{2}\right]\) mixed with dinitrogen tetroxide was used to power the Lunar Lander in its missions to the moon. The two components react according to the following equation: \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2} \mathrm{H}_{2}(l)+2 \mathrm{~N}_{2} \mathrm{O}_{4}(l) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{CO}_{2}(g)\) If \(150 \mathrm{~g}\) dimethylhydrazine reacts with excess dinitrogen tetroxide and the product gases are collected at \(127^{\circ} \mathrm{C}\) in an evacuated 250-L tank, what is the partial pressure of nitrogen gas produced and what is the total pressure in the tank assuming the reaction has \(100 \%\) yield?

Consider a \(1.0\) -L container of neon gas at STP. Will the average kinetic energy, average velocity, and frequency of collisions of gas molecules with the walls of the container increase, decrease, or remain the same under each of the following conditions? a. The temperature is increased to \(100^{\circ} \mathrm{C}\). b. The temperature is decreased to \(-50^{\circ} \mathrm{C}\). c. The volume is decreased to \(0.5 \mathrm{~L}\). d. The number of moles of neon is doubled.

Consider separate \(1.0\) -L gaseous samples of \(\mathrm{He}, \mathrm{N}_{2}\), and \(\mathrm{O}_{2}\), all at STP and all acting ideally. Rank the gases in order of increasing average kinetic energy and in order of increasing average velocity.

Calculate the root mean square velocities of \(\mathrm{CH}_{4}(\mathrm{~g})\) and \(\mathrm{N}_{2}(\mathrm{~g})\) molecules at \(273 \mathrm{~K}\) and \(546 \mathrm{~K}\).

A person accidentally swallows a drop of liquid oxygen, \(\mathrm{O}_{2}(l)\), which has a density of \(1.149 \mathrm{~g} / \mathrm{mL}\). Assuming the drop has a volume of \(0.050 \mathrm{~mL}\), what volume of gas will be produced in the person's stomach at body temperature \(\left(37^{\circ} \mathrm{C}\right)\) and a pressure of \(1.0 \mathrm{~atm}\) ?
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