Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains O2 gas at a pressure of 16,500 kPa at 23°C. b. What volume would the gas occupy at STP?

Verified step by step guidance

1. 1. First, we need to convert the volume from gallons to liters because the standard volume unit in chemistry is liters. We know that 1 gallon is approximately 3.78541 liters. So, multiply 55.0 gallons by 3.78541 to get the volume in liters.
2. 2. Next, we need to convert the temperature from Celsius to Kelvin because the standard temperature unit in chemistry is Kelvin. We know that Kelvin = Celsius + 273.15. So, add 273.15 to 23°C to get the temperature in Kelvin.
3. 3. Now, we can use the ideal gas law equation, 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. However, since we are comparing the same gas under two different conditions, we can use the combined gas law equation, which is (P1V1)/T1 = (P2V2)/T2, where the subscripts 1 and 2 refer to the initial and final conditions, respectively.
4. 4. We know the initial pressure (P1), volume (V1), and temperature (T1), and we want to find the final volume (V2) at standard temperature and pressure (STP). STP is defined as a temperature of 273.15 K and a pressure of 1.00 atm. However, since the pressure is given in kPa, we need to convert 1.00 atm to kPa. We know that 1.00 atm is approximately 101.325 kPa.
5. 5. Substitute the known values into the combined gas law equation and solve for V2. This will give you the volume of the gas at STP.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions and allows for calculations involving changes in state, such as volume at standard temperature and pressure (STP).

Standard Temperature and Pressure (STP)

STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm (101.3 kPa). At STP, one mole of an ideal gas occupies a volume of 22.4 liters. Understanding STP is crucial for converting gas volumes from one set of conditions to another, particularly in stoichiometric calculations.

Gas Volume Conversion

Gas volume conversion involves using the Ideal Gas Law and STP conditions to determine how the volume of a gas changes with variations in pressure and temperature. This concept is vital for solving problems that require finding the volume of a gas under different conditions, such as from high-pressure states to STP.