Question

A sample of fluorine gas occupies \(855 \mathrm{~mL}\) at \(710 \mathrm{~mm} \mathrm{Hg}\) and \(155^{\circ} \mathrm{C}\). What is the mass of the sample?

Short answer

The mass of the fluorine sample is approximately 0.855 grams.

Step-by-step solution

Convert Temperature to Kelvin

The given temperature is in Celsius. To use it in gas law calculations, it needs to be converted to Kelvin. Use the formula: \[ T(K) = T(^{ ext{°C}}) + 273.15 \] Plug in the known value: \[ T(K) = 155 + 273.15 = 428.15 \text{ K} \]

Convert Pressure to Atmospheres

The given pressure is in mmHg. To use it in gas law calculations, it needs to be converted to atmospheres. The conversion is as follows: \[ 1 \text{ atm} = 760 \text{ mmHg} \] Therefore, \[ P(\text{atm}) = \frac{710}{760} \approx 0.9342 \text{ atm} \]

Use the Ideal Gas Law to Solve for Moles

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 (\(0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}\)), and \(T\) is temperature. Substitute the given values, converting the volume from mL to L:\[ V = 0.855 \text{ L} \mathbf{,} \]thus,\[ n = \frac{PV}{RT} = \frac{(0.9342)(0.855)}{(0.0821)(428.15)} \approx 0.0225 \text{ moles} \]

Calculate Mass from Moles

To find the mass of fluorine gas, use the molar mass of F2. Fluorine gas, \(\text{F}_2\), has a molar mass of approximately \(38.00 \text{ g/mol}\).\[ \text{Mass} = n \times \text{Molar Mass} \approx 0.0225 \times 38.00 = 0.855 \text{ grams} \]

Key concepts

Gas laws

Understanding gas laws can simplify calculations related to gases, such as using the Ideal Gas Law, which is a powerful tool. The Ideal Gas Law is represented by the formula: \[ PV = nRT \]Where:

• \( P \) represents pressure,
• \( V \) is volume,
• \( n \) is the number of moles,
• \( R \) is the ideal gas constant (value: 0.0821 L atm K\(^{-1}\) mol\(^{-1}\)), and
• \( T \) is temperature in Kelvin.

The Ideal Gas Law helps determine unknown variables when others are known, such as finding the amount of moles when pressure, volume, and temperature are provided. Each term in the equation represents a specific property of the gas, making it vital to perform accurate conversions prior to solving.

Temperature conversion

Temperature conversion is crucial for gas law calculations. The most commonly used temperature unit in these calculations is Kelvin. This is because it incorporates absolute zero, where molecular movement stops entirely. To convert from Celsius to Kelvin, you add 273.15:\[ T(K) = T(\text{°C}) + 273.15 \]Remembering this conversion is key because gas laws rely on temperature being expressed in Kelvin.

• Ensures precision in calculations.
• Avoids negative values which do not make sense in gas law contexts.

Always check if temperatures in your problem are given in Celsius to convert them appropriately before applying the Ideal Gas Law.

Pressure conversion

When working with gas law equations, pressure must be in the appropriate units, typically atmospheres (atm). This is essential because the Ideal Gas Law constant \( R \) uses L atm units. To convert from mmHg to atm, use the conversion factor:

• \( 1 \text{ atm} = 760 \text{ mmHg} \)
• Formula: \( P(\text{atm}) = \frac{P(\text{mmHg})}{760} \)

Using the correct pressure unit maintains consistency and accuracy in calculations. Without this conversion, calculations using the Ideal Gas Law may yield incorrect results, as the gas constant \( R \) would not be dimensionally consistent with mmHg.

Molar mass calculation

The molar mass is vital for determining the mass of a gas sample, especially when using the number of moles calculated through the Ideal Gas Law. Fluorine gas \( \text{F}_2 \) consists of two fluorine atoms, making its molar mass approximately:

• Molar mass of one fluorine atom: \( 19.00 \text{ g/mol} \)
• Total molar mass of \( \text{F}_2 \): \( 38.00 \text{ g/mol} \)

To find the mass:\[ \text{Mass} = n \times \text{Molar Mass} \]Where \( n \) is the number of moles. This calculation ties the number of moles back to a quantity of substance, making it more tangible in experiments and exercises.