Question

What volume will 9.8 moles of sulfur hexafluoride \(\left(\mathrm{SF}_{6}\right)\) gas occupy if the temperature and pressure of the gas are \(105^{\circ} \mathrm{C}\) and 9.4 atm, respectively?

Short answer

The volume is approximately : 321.7 L.

Step-by-step solution

Convert Temperature to Kelvin

First, convert the temperature from Celsius to Kelvin because gas law calculations require absolute temperature. Use the formula \( T(K) = T(°C) + 273.15 \). Here, the temperature is 105°C, so \( T(K) = 105 + 273.15 = 378.15 \) K.

Identify the Ideal Gas Law

We will use the Ideal Gas Law, which is \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.We are given \( P = 9.4 \) atm, \( n = 9.8 \) moles, and \( T = 378.15 \) K. The ideal gas constant \( R \) can be used as \( 0.0821 \) L·atm/(K·mol).

Rearrange the Ideal Gas Law to Solve for Volume

Rearrange the Ideal Gas Law to solve for volume \( V \):\[ V = \frac{nRT}{P} \]

Substitute the Values and Calculate

Substitute the known values into the rearranged formula:\[ V = \frac{9.8 \times 0.0821 \times 378.15}{9.4} \]Calculate this to find the volume \( V \).

Key concepts

Moles to Volume Conversion

In chemistry, the Ideal Gas Law helps us connect various properties of gases, specifically how moles relate to volume. This is vital because in real-world processes, understanding how much space a certain amount of gas will occupy is extremely useful. When you know the number of moles () of a gas, along with its temperature and pressure, you can determine the volume (V) using the formula from the Ideal Gas Law: \[ V = \frac{nRT}{P} \] where:

• V is the volume of the gas
• n is the number of moles
• R is the ideal gas constant
• P is the pressure
• T is the temperature in Kelvin

Plug in these values, and you can find the volume a particular amount of gas occupies. This understanding is important for calculating how gases will behave under different conditions, like changes in volume or pressure.

Temperature Conversion to Kelvin

Temperature plays a critical role in the behavior of gases, and the Ideal Gas Law requires temperature to be in Kelvin. The Kelvin scale starts at absolute zero and ensures no negative numbers are involved. Converting Celsius to Kelvin is simple:

• Use the formula: \( T(K) = T(°C) + 273.15 \)
• For example, if the temperature is 105°C, adding 273.15 gives you 378.15 K.

Using Kelvin avoids mathematical complexities that arise with negative values and aligns with scientific standards. This conversion ensures precise and accurate calculations when using gas laws.

Pressure in atm

Pressure is a measure of how much force is applied over an area and is a critical factor in the Ideal Gas Law. Atmospheric pressure (atm) is a common unit for pressure and is often used in chemistry for calculations involving gases. When conducting gas law calculations:

• Use pressure in atmospheres to align with the standard Ideal Gas Law formula.
• If your pressure is given in another unit, such as Pascals or mmHg, you may need to convert it to atm to make calculations easier.

In our example, using 9.4 atm makes the problem straightforward since we don’t need to convert pressure. Remembering the importance of pressure will help you understand how it influences gas volume and behavior.

Ideal Gas Constant

The ideal gas constant, denoted as R, is a key component in the Ideal Gas Law. It relates the pressure, volume, temperature, and moles of a gas. The constant is expressed in several units, but for standard calculations in chemistry, we often use \( R = 0.0821 \) L·atm/(K·mol). Here’s why this constant is essential:

• It balances the units of the equation so that when you calculate \( PV = nRT \), all measurements align correctly.
• Different scenarios may require different values depending on the units used. For example, if pressure is measured in Pascals, you would use a different value of R.

Understanding R helps correctly apply the Ideal Gas Law, especially when solving for one unknown variable, such as the volume of gas in a specific calculation.