Problem 22 - Chemistry and Chemical Reactivity

Question

What mass of helium, in grams, is required to fill a 5.0 -L balloon to a pressure of 1.1 atm at \(25^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

0.892 grams of helium are needed.

Step 1: Identify the given variables

The problem provides the following information:- Volume of the balloon, \( V = 5.0 \text{ L} \).- Pressure, \( P = 1.1 \text{ atm} \).- Temperature, \( T = 25^{\circ} \text{C} \).

Step 2: Convert temperature to Kelvin

We need to convert the temperature from degrees Celsius to Kelvin to use it in the Ideal Gas Law. The conversion formula is: \( T(K) = T(^{\circ}C) + 273.15 \).\[ T = 25 + 273.15 = 298.15 \text{ K} \]

Step 3: Use the Ideal Gas Law

The Ideal Gas Law relates pressure, volume, temperature, and number of moles: \( PV = nRT \).Where:- \( R \) is the ideal gas constant, \( R = 0.0821 \text{ L atm K}^{-1} \text{mol}^{-1} \).We need to solve for \( n \) (the number of moles):\[ n = \frac{PV}{RT} \]

Step 4: Calculate the number of moles of helium

Substitute the given values into the rearranged Ideal Gas Law formula:\[ n = \frac{(1.1 \text{ atm})(5.0 \text{ L})}{(0.0821 \text{ L atm K}^{-1} \text{mol}^{-1})(298.15 \text{ K})} \]\[ n \approx 0.223 \text{ moles} \]

Step 5: Convert moles to grams

The molar mass of helium is approximately \( 4.00 \text{ g/mol} \). To find the mass in grams, multiply the number of moles by the molar mass:\[ \text{mass} = n \times \text{molar mass} = 0.223 \text{ moles} \times 4.00 \text{ g/mol} = 0.892 \text{ g} \]

Key Concepts

Helium Gas

Helium is a very light and unreactive noble gas. It is the second lightest and second most abundant element in the observable universe, primarily occurring in stars.
It is well-known for its low density, which makes it ideal for filling balloons and airships. Another unique feature of helium is that it does not easily form chemical compounds due to its complete electron shell.

• Helium being a noble gas means it is non-toxic and inert, making it a safe option for scientific and leisure purposes.
• Understanding the properties of helium helps in calculating its mass and moles under various conditions using gas laws.

These properties play a crucial role in understanding how gases behave, making helium a classic subject in many gas law calculations.

Moles Calculation

Moles are a fundamental unit in chemistry used to express amounts of a chemical substance. The number of moles of a gas can be calculated using the Ideal Gas Law.
In the context of the problem, you need to find how many moles of helium are required to fill a balloon.
The Formula

• The Ideal Gas Law formula is: \( PV = nRT \)
• In this formula, \( n \) is the number of moles, \( P \) is the pressure, \( V \) is the volume, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Using this equation, we can solve for \( n \), the moles of helium. Once we have the moles, converting to grams is simple by multiplying by helium's molar mass, which is roughly 4.00 g/mol. This marks a critical step in many chemistry problems involving gases.

Gas Laws

Gas laws are essential rules for understanding how gases behave under different conditions of pressure, volume, and temperature. The Ideal Gas Law is one of the most important.
This formula combines several simpler gas laws, like Boyle's law and Charles's law, into a single equation.

• Boyle's Law: States the inverse relationship between pressure and volume at constant temperature.
• Charles's Law: States the direct relationship between volume and temperature at constant pressure.

By bringing these laws together, the Ideal Gas Law \( PV = nRT \) offers a comprehensive tool for predicting and understanding gas behavior. When using real gases like helium, this law helps predict how changes in one condition can affect others.

Temperature Conversion

Temperature conversion is often necessary when applying the Ideal Gas Law because it requires temperature in Kelvin.
Kelvin is used because it is an absolute temperature scale that starts at absolute zero, where molecular motion ceases.
Conversion Formula

• To convert Celsius to Kelvin: \( T(K) = T(°C) + 273.15 \)
• For example, to convert 25°C to Kelvin, is simply: \( 25 + 273.15 = 298.15 \text{ K} \)

This conversion ensures the temperature aligns with the scales used for scientific calculations, allowing accurate predictions of gas behavior every time you use the Ideal Gas Law.