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Ch.8 Gases
Timberlake - Chemistry: An Introduction to General, Organic, and Biological Chemistry 13th Edition
Timberlake13th EditionChemistry: An Introduction to General, Organic, and Biological ChemistryISBN: 9780134421353Not the one you use?Change textbook
Chapter 8, Problem 71

In 1783, Jacques Charles launched his first balloon filled with hydrogen gas, which he chose because it was lighter than air. If the balloon had a volume of 31 000 L, how many kilograms of hydrogen were needed to fill the balloon at STP?
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Step 1: Recall the conditions of STP (Standard Temperature and Pressure). At STP, the temperature is 273.15 K, the pressure is 1 atm, and 1 mole of any ideal gas occupies 22.4 L.
Step 2: Use the volume of the balloon (31,000 L) and the molar volume of a gas at STP (22.4 L/mol) to calculate the number of moles of hydrogen gas. The formula is: \( \text{moles of H}_2 = \frac{\text{volume of H}_2}{\text{molar volume at STP}} \).
Step 3: Determine the molar mass of hydrogen gas (H₂). Since each hydrogen atom has a molar mass of approximately 1.008 g/mol, the molar mass of H₂ is \( 2 \times 1.008 = 2.016 \ \text{g/mol} \).
Step 4: Convert the moles of hydrogen gas to grams using the formula: \( \text{mass of H}_2 = \text{moles of H}_2 \times \text{molar mass of H}_2 \).
Step 5: Convert the mass of hydrogen gas from grams to kilograms by dividing by 1,000. The formula is: \( \text{mass in kg} = \frac{\text{mass in g}}{1000} \).

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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 in Kelvin. This law allows us to calculate the amount of gas needed under specific conditions, such as Standard Temperature and Pressure (STP).
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Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a reference point used in chemistry to define the conditions under which gas measurements are made. STP is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (101.3 kPa). At STP, one mole of an ideal gas occupies a volume of 22.4 liters, which is crucial for calculating the amount of gas required to fill a given volume.
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Molar Mass of Hydrogen

The molar mass of hydrogen is the mass of one mole of hydrogen gas (H2), which is approximately 2 grams per mole. This value is essential for converting between the volume of hydrogen gas and its mass when using the Ideal Gas Law. Knowing the molar mass allows us to determine how many kilograms of hydrogen are needed to fill the balloon at STP based on the volume provided.
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Related Practice
Textbook Question

A balloon is filled with helium gas with a partial pressure of 1.00 atm and neon gas with a partial pressure of 0.50 atm. For each of the following changes (a to e) of the initial balloon, select the diagram (A, B, or C) that shows the final volume of the balloon:

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d. The Kelvin temperature doubles and half of the gas atoms leak out (P does not change).

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Textbook Question

Indicate if pressure increases, decreases, or stays the same in each of the following:

a.

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Textbook Question

At a restaurant, a customer chokes on a piece of food. You put your arms around the person's waist and use your fists to push up on the person's abdomen, an action called the Heimlich maneuver.

b. Why does it cause the person to expel the food item from the airway?

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Textbook Question

A weather balloon is partially filled with helium to allow for expansion at high altitudes. At STP, a weather balloon is filled with enough helium to give a volume of 25.0 L. At an altitude of 30.0 km and –35 ⁰C, it has expanded to 2460 L. The increase in volume causes it to burst and a small parachute returns the instruments to Earth.

b. What is the final pressure, in millimeters of mercury, of the helium inside the balloon when it bursts?

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Textbook Question

A mixture of nitrogen (N2) and helium has a volume of 250 mL at 30 °C and a total pressure of 745 mmHg.

a. If the partial pressure of helium is 32 mmHg, what is the partial pressure of the nitrogen?

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Textbook Question

What is the total pressure, in millimeters of mercury, of a gas mixture containing argon gas at 0.25 atm, helium gas at 350 mmHg, and nitrogen gas at 360 Torr?

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