Question

A sample of oxygen gas has a volume of 125 L at \(25^{\circ} \mathrm{C}\) and a pressure of 0.987 atm. Calculate the volume of this oxygen sample at STP.

Short answer

The volume of the oxygen gas at STP is approximately 113.8 L.

Step-by-step solution

Convert temperature to Kelvin

Temperature in Celsius is given as 25°C. To convert this to Kelvin (K), we will use the conversion formula: Temperature(K) = Temperature(°C) + 273.15 So, the temperature in Kelvin will be: Temperature(K) = 25°C + 273.15 = 298.15 K

Convert pressure to kPa

The pressure of the gas is given in atm (atmospheres). We will convert this to kPa (kilopascals) using the conversion factor 1 atm = 101.325 kPa. Pressure (kPa) = Pressure (atm) × 101.325 Pressure (kPa) = 0.987 atm × 101.325 = 100 kPa

Find the number of moles (n) using the Ideal Gas Law

Now we can use the Ideal Gas Law to find the number of moles (n) of the gas: PV = nRT Where: P = pressure (kPa), V = volume (L), n = number of moles, R = ideal gas constant (R = 8.314 J/mol*K), T = temperature (K) We can rearrange the equation to solve for the number of moles: n = PV / (RT) and plug in the known values: n = (100 kPa × 125 L) / (8.314 J/mol*K × 298.15 K) n = 5.03 moles (approx)

Calculate the final volume at STP

We will now use the ideal gas law again to calculate the final volume at Standard Temperature and Pressure (STP). STP conditions are 0°C (273.15 K) and 100 kPa. Since we're solving for the final volume (V'), we can form the equation: P'V' = nRT' Where: P' = final pressure (STP = 100 kPa), V' = final volume, n = number of moles (calculated in Step 3), R = ideal gas constant (R = 8.314 J/mol*K), T' = final temperature (STP = 273.15 K) We can rearrange the equation to solve for the final volume: V' = nRT' / P' and plug in the known values: V' = (5.03 moles × 8.314 J/mol*K × 273.15 K) / 100 kPa V' ≈ 113.8 L The volume of the oxygen gas at STP is approximately 113.8 L.

Key concepts

Gas Volume Calculations

Gas volume calculations involve determining the volume a gas will occupy under various conditions. It's essential to understand how factors like pressure, temperature, and the number of gas molecules affect volume. The Ideal Gas Law, expressed as \(PV = nRT\), is a powerful tool for these calculations.

• \(P\) stands for pressure, \(V\) for volume, \(n\) for the number of moles of gas, \(R\) the ideal gas constant, and \(T\) the temperature in Kelvin.
• This formula helps us relate volume with other gas properties like moles, temperature, and pressure.

When calculating how the volume changes under conditions like Standard Temperature and Pressure (STP), we use this law to account for those changes.
STP is defined as 0°C (273.15 K) and 100 kPa. With a known initial volume and conditions, you can determine a gas's volume at STP using the Ideal Gas Law.

Pressure Conversion

Pressure conversion is often needed when dealing with gas calculations, to ensure all measurements align with the units in the Ideal Gas Law. In our example, pressure was initially given in atmospheres (atm), which needed conversion to kilopascals (kPa). This is a common unit of pressure in many scientific equations.

• Convert atm to kPa using the conversion factor: 1 atm = 101.325 kPa.
• The calculation involves multiplying pressure in atm by 101.325 to yield pressure in kPa.

Understanding how to switch between pressure units is crucial, as incorrect conversions can lead to incorrect results. Remember, always ensure pressure units match those required by the gas constant used in your calculations.

Temperature Conversion

Temperature conversion, especially from Celsius to Kelvin, is vital in implementing the Ideal Gas Law correctly. Most gas laws require temperature to be in Kelvin. This unit is preferred because it begins at absolute zero, aligning with the laws of thermodynamics.

• Convert Celsius to Kelvin using the formula: Temperature(K) = Temperature(°C) + 273.15.
• In the given exercise, this means adding 273.15 to 25°C, giving 298.15 K.

Converting temperatures ensures consistency in calculations and helps in accurately assessing how temperature changes influence gas behavior. Always verify the temperature unit before starting any gas-related computations.