Question

A 160.0 -L helium tank contains pure helium at a pressure of 1855 psi and a temperature of 298 K. How many 3.5 -L helium balloons will the helium in the tank fill? (Assume an atmospheric pressure of 1.0 atm and a temperature of 298 K.)

Short answer

The helium tank can fill a certain number of 3.5-L helium balloons depending on the amount of helium in moles contained within the tank. After performing the calculation with the ideal gas law, divide the total moles of helium in the tank by the moles of helium needed per balloon to find the exact number.

Step-by-step solution

Convert tank pressure to atm

Convert the pressure of the helium in the tank from psi to atm using the conversion factor: 1 atm = 14.6959 psi. Calculate the pressure in atm using the formula: Pressure (atm) = Pressure (psi) / Conversion factor.

Apply the Ideal Gas Law for the tank

Use the Ideal Gas Law in the form of PV = nRT to calculate the moles (n) of helium in the tank initially. For Helium tank: P = converted pressure in atm, V = 160.0 L, R = 0.0821 Latm/Kmol, T = 298 K.

Calculate moles of helium in the tank

Rearrange the Ideal Gas Law to solve for n (moles of helium). n = PV / RT. Use the pressure calculated in Step 1 and plug in the values into the formula to get the moles of helium.

Apply the Ideal Gas Law for one balloon

Repeat the use of the Ideal Gas Law for one 3.5-L balloon. Since the balloon will be filled at atmospheric pressure of 1.0 atm and the same temperature of 298 K, solve for 'n' with V = 3.5 L, P = 1.0 atm, R = 0.0821 Latm/Kmol, T = 298 K.

Calculate moles of helium per balloon

Rearrange the Ideal Gas Law to solve for n (moles of helium in one balloon). n = PV / RT. Use P = 1.0 atm, V = 3.5 L, and the constant values for R and T to get the n.

Calculate the number of balloons the tank can fill

Divide the total moles of helium in the tank by the moles of helium per balloon. This will give you the number of balloons that can be filled.

Key concepts

Gas Pressure Conversion

Understanding gas pressure conversion is essential for students studying chemistry, as it allows for the comparison and calculation of pressures in different units. In our exercise, converting the pressure of helium from pounds per square inch (psi) to atmospheric pressure (atm) was the first step. The conversion factor used is 1 atm = 14.6959 psi.

This is a crucial step because most equations in chemistry, including the Ideal Gas Law, commonly use atm as the unit for pressure. Being able to convert between units is an invaluable skill in the laboratory and various scientific applications. For example, if you have a pressure reading in psi, you simply divide it by 14.6959 to find its equivalent in atm. Conversely, to convert from atm to psi, you'd multiply the atm value by 14.6959.

Molar Volume

The molar volume of an ideal gas is the volume that one mole of the gas occupies at a given temperature and pressure. According to the Ideal Gas Law (\( PV = nRT \)), if the gas behaves ideally, you can find the molar volume by rearranging the equation to solve for volume (\( V \)) with n (number of moles) set to 1.

At standard temperature and pressure (0°C and 1 atm), the molar volume for any ideal gas is approximately 22.4 liters. This concept is crucially important when you are trying to determine how much gas can be produced or required in a reaction (stoichiometry of gases). By understanding the molar volume, students can determine the volume of gas involved, either being produced or consumed, in a given reaction.

Stoichiometry of Gases

Stoichiometry of gases involves using balanced chemical equations to calculate the volume, mass, or number of moles of gases involved in chemical reactions. It is a subsection of stoichiometry, which is the quantitative relationship between reactants and products in a chemical reaction.

To solve stoichiometric problems for gases, we often use the Ideal Gas Law. The law correlates the pressure, volume, temperature, and number of moles of a gas. In our example, we first found the moles of helium in both the tank and a single balloon. After that, the stoichiometry comes into play by allowing us to calculate how many balloons can be filled with the gas in the tank. This application of gas stoichiometry is vital in fields such as chemical engineering and environmental science.

Standard Atmospheric Pressure

Standard atmospheric pressure is a commonly used reference pressure in various scientific fields. It is defined as the pressure exerted by a column of mercury 760 mm high (also expressed as 101.325 kPa) at sea level at a temperature of 0°C. This unit of pressure, 1 atm, is a key component in many gas law applications, including the calculations we performed in our exercise.

In everyday language, atmospheric pressure is what we simply call 'air pressure,' and it influences everything from weather systems to the breathing of living organisms. When working with gases, it's often necessary to consider the pressure at which gas reactions and processes occur, as this can significantly impact the outcomes. Thus, understanding and applying the concept of standard atmospheric pressure is crucial for accurate experimentation and problem-solving in gas chemistry.