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Ch.10 - Gases
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBrown 14th EditionCh.10 - GasesProblema 44c
Capitolo 10, Problema 44c

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (c) At what temperature would the pressure in the tank equal 15.2 MPa?

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First, we need to understand that this problem is about the gas laws, specifically the Gay-Lussac's law which states that the pressure of a gas is directly proportional to its absolute temperature, provided the volume is kept constant. In mathematical terms, this can be expressed as P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Next, we need to convert all the given values to the appropriate units. The initial pressure (P1) is given as 16,500 kPa, which we need to convert to MPa by dividing by 1000. The initial temperature (T1) is given as 23 °C, which we need to convert to Kelvin by adding 273.15. The final pressure (P2) is given as 15.2 MPa, which is already in the correct units.
Then, we can substitute the known values into the Gay-Lussac's law equation. We have P1/T1 = P2/T2, so we can rearrange the equation to solve for the final temperature (T2): T2 = P2 * T1 / P1.
Substitute the known values into the equation for T2. Remember to use the converted values for P1, T1, and P2.
Finally, solve the equation to find the final temperature (T2). This will give you the temperature at which the pressure in the tank would equal 15.2 MPa.

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Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to predict how changing one of these variables affects the others, making it essential for solving gas-related problems.
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Pressure Units Conversion

Understanding pressure units is crucial when working with gas laws. In this context, pressure is given in kilopascals (kPa) and megapascals (MPa), where 1 MPa equals 1,000 kPa. Properly converting between these units is necessary to ensure accurate calculations when determining the conditions of the gas in the tank, especially when comparing initial and final pressures.
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Pressure Units

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Although the problem involves changing pressure, understanding this relationship helps in grasping how temperature affects gas behavior. In this case, as the pressure decreases, the temperature must also change, which can be calculated using the Ideal Gas Law.
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Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (d) What would be the pressure of the gas, in kPa, if it were transferred to a container at 24 °C whose volume is 55.0 L?

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Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (a) What mass of O2 does the tank contain?

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Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?

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