Question

How many moles of helium gas (He) would be required to fill a 22-L container at a temperature of 35°C and a pressure of 3.1 atm?

Short answer

Approximately \(2.72\) moles of helium gas would be required to fill the \(22\)-L container at \(35°C\) and \(3.1\) atm pressure.

Step-by-step solution

1. Convert Temperature to Kelvin

To find the temperature in Kelvin, add 273.15 to the given temperature in Celsius: T(K) = T(°C) + 273.15 T(K) = 35°C + 273.15 = 308.15 K

2. Rearrange Ideal Gas Law Formula for n

Now, rearrange the Ideal Gas Law Formula to isolate n: n = PV / RT

3. Plug in the Given Values and Solve for n

With the formula rearranged, plug in the given values: P = 3.1 atm V = 22 L R = 0.0821 L atm / K mol (Ideal Gas Constant) T = 308.15 K n = (3.1 atm × 22 L) / (0.0821 L atm / K mol × 308.15 K) n ≈ 2.72 mol So, approximately 2.72 moles of helium gas would be required to fill the 22-L container at 35°C and 3.1 atm pressure.

Key concepts

Helium Gas

Helium gas, often represented as He, is the second lightest and second most abundant element in the observable universe. It is a noble gas, which means it doesn't easily react with other elements. This makes helium a great choice for applications where non-reactivity is essential, such as in balloons, airships, and as a protective gas in welding.

Helium is colorless, tasteless, and odorless, and it does not catch fire. In fact, when thinking about filling a container with helium, it is critical to note that helium doesn't bind with other substances, ensuring it remains pure. When calculating moles of helium required to fill a container, it's essential to know the pressure and temperature as these impact gas behavior significantly, according to the Ideal Gas Law. Thus, understanding the chemical and physical nature of helium helps grasp why conditions like temperature and pressure influence calculations.

Moles Calculation

Calculating moles is at the heart of using the Ideal Gas Law. A mole represents a specific number of particles of a substance, typically used in chemistry to express amounts of a chemical substance. According to Avogadro's number, one mole equals approximately 6.022 x 10^{23} particles.

The Ideal Gas Law formula used for calculating the number of moles is: \( PV = nRT \) This equation helps establish a relationship between pressure (P), volume (V), moles (n), the ideal gas constant (R), and temperature (T). Rearranging the formula to solve for moles gives us: \( n = \frac{PV}{RT} \)

By using this equation, you can calculate how many moles are present in a particular gas sample under specified conditions. Plugging in the values for pressure, volume, and temperature lets you determine the amount of substance needed to fill your container with the gas in question, which in this exercise, is helium.

Temperature Conversion

Temperature conversion is a fundamental step when working with gas laws because these calculations require temperature to be in Kelvin. Kelvin is an absolute temperature scale that starts from absolute zero, the theoretical point where molecular motion stops.

To convert between Celsius and Kelvin, you can use the following equation: \( T(K) = T(°C) + 273.15 \)

In this exercise, the given temperature was 35°C, which converts to 308.15 K on the Kelvin scale. Always remember to use Kelvin when applying the Ideal Gas Law, as it provides a consistent baseline that is required for accurate calculations. Temperature directly impacts the behavior of gas particles; thus, proper conversion ensures the correctness of your calculations.