Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O 2 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?

Hey everyone in this example, we're told that a gas container with the volume 300 liters contains five bars of nitrogen gas at 20 degrees Celsius. We need to calculate the temperature at which our nitrogen gas in the container is 8. bars. So we want to recall that for this type of question. We're going to use dig a loose tax law where we take our initial pressure, divide that by our initial temperature and set that equal to our final pressure divided by our final temperature. For the purpose of solving this question, we're going to reorganize this law so that we have our initial pressure multiplied by the final pressure set equal to our final pressure, multiplied by our initial temperature. And what we would have plugging in the info from the prompt is our initial pressure given as five bars from the question. Were then multiplying this by our final temperature, which is what we need to solve for. So that's T two Set equal to our final pressure given in the prompt as 8.60 bars. And then multiplied by our initial temperature given in the prompt as 20°C. However, we want this to be in Kelvin. So we're going to add to 73.15. So simplifying this, we would have five bars. Our initial pressure multiplied by the final temperature of our container equal to a value of the product of the right hand side, which is going to equal 2521.09. And our units are now bars, times kelvin. So we want to go ahead and isolate for the final temperature by dividing both sides by five bars. And so this allows us to cancel our units of bars, leaving us with Kelvin as our final unit, which is what we want for temperature and what we're going to get is that our final temperature of our container is equal to a value of 504. Kelvin. Now, we want to go ahead and convert this back to Celsius. So we're going to subtract 2 73.15 and this is going to give us our final answer in Celsius of 31 point oh seven degrees Celsius as our final temperature of our container. And this is going to be our final answer to complete this example. So I hope that everything I went through is clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

Problem 44c

Chapter 10, Problem 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?

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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Charles's Law

Related Practice

Textbook Question

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 119.3 kPa and 24 °C. (d) At what pressure will the volume equal 5.00 L if the temperature is 58 °C?

Textbook Question

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?

Textbook Question

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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Textbook Question

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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Textbook Question

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 30 minutes the average cockroach (running at 0.08 km/h) consumed 1.0 mL of O₂ at 101.33 kPa pressure and 20 °C per gram of insect mass. (a) How many moles of O₂ would be consumed in 1 day by a 6.3-g cockroach moving at this speed?

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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. (c) At what temperature would the pressure in the tank equal 15.2 MPa?

Verified video answer for a similar problem:

Key Concepts

Ideal Gas Law

Pressure Units Conversion

Charles's Law

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?