A 6.0-L tank is filled with helium gas at a pressure of 2 MPa. How many balloons (each 2.00 L) can be inflated to a pressure of 101.3 kPa, assuming that the temperature remains constant and that the tank cannot be emptied below 101.3 kPa?

Verified step by step guidance

Step 1: Use the ideal gas law to determine the initial number of moles of helium in the tank. The ideal gas law is given by 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. Since temperature is constant, you can rearrange the equation to solve for n: n = PV/RT.

Step 2: Calculate the initial moles of helium in the tank using the given pressure (2 MPa), volume (6.0 L), and convert the pressure to the same units as the final pressure (kPa) for consistency. Use R = 8.314 J/(mol·K) and convert the volume to cubic meters if necessary.

Step 3: Determine the final pressure in the tank when it cannot be emptied below 101.3 kPa. Subtract this pressure from the initial pressure to find the usable pressure difference for inflating the balloons.

Step 4: Calculate the number of moles of helium that can be used to inflate the balloons using the usable pressure difference and the initial volume of the tank. Use the ideal gas law again to find the moles of helium that correspond to this pressure difference.

Step 5: Calculate the number of balloons that can be inflated by dividing the total moles of helium available for inflation by the moles required to fill one balloon at 101.3 kPa and 2.00 L. Use the ideal gas law to find the moles needed for one balloon.

Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions and allows us to calculate the amount of gas in a given volume at a specific pressure and temperature.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant (P1V1 = P2V2). This principle is crucial for solving problems involving gas expansion or compression, such as inflating balloons from a gas tank.

Gas Stoichiometry

Gas stoichiometry involves using the relationships between the amounts of reactants and products in a chemical reaction, specifically in terms of gas volumes. In this context, it helps determine how many balloons can be inflated from a given volume of gas at different pressures, ensuring that the calculations account for the gas's behavior under varying conditions.

Recommended video:

Guided course

00:47

Gas Stoichiometry Concepts

Related Practice

Textbook Question

Calculate the pressure that CCl₄ will exert at 80 °C if 1.00 mol occupies 33.3 L, assuming that (a) CCl₄ obeys the ideal-gas equation (b) CCl₄ obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.)

Textbook Question

Table 10.3 shows that the van der Waals b parameter has units of L/mol. This means that we can calculate the sizes of atoms or molecules from the b parameter. Refer back to the discussion in Section 7.3. Is the van der Waals radius we calculate from the b parameter of Table 10.3 more closely associated with the bonding or nonbonding atomic radius discussed there? Explain.

Textbook Question

A gas bubble with a volume of 1.0 mm³ originates at the bottom of a lake where the pressure is 3.0 atm. Calculate its volume when the bubble reaches the surface of the lake where the pressure is 730 torr, assuming that the temperature does not change.

Textbook Question

Carbon dioxide, which is recognized as the major contributor to global warming as a “greenhouse gas,” is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6×106 tons of CO2 per year. a. Assuming ideal-gas behavior, 1.00 atm, and 27°C, calculate the volume of CO2 produced by this power plant.

Textbook Question

Nickel carbonyl, Ni(CO)4, is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8-h workday is 1 ppb (parts per billion) by volume, which means that there is one mole of Ni(CO)4 for every 109 moles of gas. Assume 24°C and 1.00 atm pressure. What mass of Ni(CO)4 is allowable in a laboratory room that is 12ft×20ft×9ft?

Textbook Question

Consider the arrangement of bulbs shown in the drawing. Each of the bulbs contains a gas at the pressure shown. What is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (We can neglect the volume of the capillary tubing connecting the bulbs.)

views