Carbon dioxide, which is recognized as the major contributor to global warming as a “greenhouse gas,” is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO 2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6⨉10 6 tons of CO 2 per year. (b) If the CO 2 is stored underground as a liquid at 10 C and 12.16 MPa and a density of 1.2 g/cm 3 , what volume does it possess?

Hi everyone for this problem, we're told that nitric acid can be obtained from the reaction of nitrogen dioxide and water. The net reaction is shown below. Initially a 2.55 liter reaction vessel is filled with nitrogen dioxide gas at 1.5 A. T. M. And 28 degrees Celsius, calculate the volume of nitric acid produced from the reaction. Note that the density of nitric acid is 1.51 g per millimeter. So for this problem, we want to calculate the volume of nitric acid and something that we're going to need to remember in order to solve this problem is the ideal gas law, which tells us that P. V. Is equal to N. R. T. And what we can do here is we can, because we're given the density, we can calculate the volume using density. But first we need to solve for moles of and 02. And so we're going to go from moles of N 02, two mass of N 02. And then we can use our density to solve for our volume. Okay, so that's what's mapped out. So let's rearrange our ideal gas law so that we can solve for moles. Okay, so if we divide, I'm going to move this down. If we divide our ideal gas law by R. T. On both sides, we're going to get N. Which is our moles is equal to P. V over R. T. So that's where we're going to start. So let's start off by finding what is our pressure or plugging in what we are given. Okay, So we have our pressure we're told is 1.5 a T. M. And we're going to multiply that by B which is volume. And we're told that we have a 2.55 liter reaction vessel. Okay. And this is going to be over to move this over here. Our is our gas constant, which is zero point 08206 leaders per atmosphere over more times kelvin. And so this is a constant. So this is something that we should know. It wasn't given in the problem. And then our temperature because r universal gas constant is in kelvin and we're told that we have 28 degrees Celsius, we need to convert 28 degrees Celsius to kelvin and we can do that by adding so degrees Celsius plus 273.15 gives us 301.15 kelvin. So we needed to convert that first so we can plug that in 301.15 kelvin. So now we have everything that we need to solve four moles. So once we plug this in we get our mold is equal to zero point 1083 most as and 02. Okay, so now we have our moles of N L two and now we need to go to mass of N 02. So we can find our mass of N 02 from moles by using our multiple ratio and moller mass. So let's go ahead and do that. And so we have we just saw for our moles of N 02. So let's look at our reaction. We need to go from moles of N 02, two g of nitric acid. Because that's what we're looking for. We're looking for nitric acid. What is our multiple ratio of N 02 to nitric acid? When we look at our reaction, we're looking at N. 02 and nitric acid. And so we have to most of nitric acid for every three moles of N 02. And so are moles of N. O. To cancel. And we're going to be left with this should say most of H N 03. Let me rewrite that so we can see our units clearly. So two moles H and three. Okay, so two moles of nitric acid. So now we have moles of nitric acid but we want mass of nitric acid. So we need to look up the molar mass. And so in one mole of nitric acid using our periodic table, we see that our molar mass is 63 point 018 g of nitric acid. Okay, so let's look at our units. We see that moles of nitric acid cancel. And we're left with mass of nitric acid. So when we saw for this we get four, this is going to equal four point 549, nine g of nitric acid. So now that we have our mass of nitric acid, we can go to volume by using density. Okay, They were told that the density of nitric acid is 1.51 g per milliliter. We can say that we can use that unit conversion here and one millimeter. There is one point g of nitric acid and that's were that's from our density. And so when we solve that, that is going to give us our volume because our grams of nitric acid canceled and will be left with MIl leaders. So once we solve this we get 3. middle leaders is our volume. And this is our final answer. This is the volume of nitric acid produced from the reaction. That's the end this problem. I hope this was helpful.

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

Problem 101b

Chapter 10, Problem 101b

Carbon dioxide, which is recognized as the major contributor to global warming as a “greenhouse gas,” is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO₂ added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6⨉10⁶ tons of CO₂ per year. (b) If the CO₂ is stored underground as a liquid at 10 C and 12.16 MPa and a density of 1.2 g/cm³, what volume does it possess?

Verified step by step guidance

First, convert the mass of CO2 from tons to grams. Since 1 ton is equal to 1,000,000 grams, multiply the given mass of CO2 (6⨉10^6 tons) by 1,000,000 to get the mass in grams.

Next, use the formula for density, which is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), to solve for the volume. Rearrange the formula to \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Substitute the mass in grams and the given density (1.2 g/cm^3) into the rearranged formula to calculate the volume in cubic centimeters.

Convert the volume from cubic centimeters to cubic meters. Since 1 cubic meter is equal to 1,000,000 cubic centimeters, divide the volume in cubic centimeters by 1,000,000 to get the volume in cubic meters.

Finally, ensure that all units are consistent and check your calculations for any errors. The volume calculated will be the volume of CO2 stored underground as a liquid at the given conditions.

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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 relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. While the question involves CO2 in a liquid state, understanding gas behavior under varying conditions is crucial for grasping how gases can be compressed and stored. This law helps predict how changes in temperature and pressure affect gas volume.

Density and Volume Relationship

Density is defined as mass per unit volume (density = mass/volume). In this context, knowing the density of liquid CO2 allows us to calculate its volume when a specific mass is given. This relationship is essential for converting the mass of CO2 produced by the power plant into a volume that can be stored underground.

Phase Changes of Substances

Phase changes refer to the transitions between solid, liquid, and gas states of matter, influenced by temperature and pressure. In this scenario, CO2 is stored as a liquid at a specific temperature and pressure, which is critical for understanding how it behaves and can be effectively stored. Recognizing the conditions under which CO2 remains in liquid form is vital for the calculations involved.

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A gas bubble with a volume of 1.0 mm³ originates at the bottom of a lake where the pressure is 3.0 atm. Calculate its volume when the bubble reaches the surface of the lake where the pressure is 730 torr, assuming that the temperature does not change.

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Textbook Question

Carbon dioxide, which is recognized as the major contributor to global warming as a 'greenhouse gas,' is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO₂ added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6×10⁶ tons of CO₂ per year. (a) Assuming ideal-gas behavior, 101.3 kPa, and 27 °C, calculate the volume of CO₂ produced by this power plant.

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Consider the arrangement of bulbs shown in the drawing. Each of the bulbs contains a gas at the pressure shown. What is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (We can neglect the volume of the capillary tubing connecting the bulbs.)

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