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. (a) Assuming ideal-gas behavior, 101.3 kPa, and 27 °C, calculate the volume of CO 2 produced by this power plant.

Hi everyone for this problem, we're told cement is the source of about 8% of the world's carbon dioxide emissions. The manufacturer of cement produces about .9 kg of carbon dioxide for every two kg of cement In 2021, 92 million metric tons of cement were produced in the United States. We need to calculate the volume of carbon dioxide emitted by cement production in the US in 2021. Assume that it behaves as an ideal gas under the conditions of 1 80 M and 25 degrees Celsius. So, our mission here is to calculate the volume of carbon dioxide emitted by cement production. Okay. And we're going to assume that it behaves as an ideal gas. So we need to recall the ideal gas law here and that is PV equals N R T. And we're looking to calculate volume. So we need to isolate this ideal gas law to solve for volume and we do that by dividing both sides by peak. So our equation that we're solving for here is volume is equal to N R T over P. So let's go ahead and get started. We want to know the volume of carbon dioxide emitted by cement production in the us and 2021. So how much cement Production did we have in 2021? That's going to be our starting point. So we had Million metric tons. OK, so let's go ahead and write that down. So we have 92 Million metric tons as an exponent is going to be 92 times 10 to the six tons. This is metric tons. Okay, so metric tons of cement. So we want to go from metric tons of cement to moles of carbon dioxide because n is moles. So in order to solve for moles, we need to convert from metric tons of cement, two moles of carbon dioxide. So let's go ahead and start off by converting this metric tons of cement to grams. Okay, Because once we do that, we can use the molar mass of carbon dioxide along with a multiple conversion. So that's going to be our first thing. So one metric ton is equal to kilograms. Okay, remember we're going from we're trying to go from metric tons to grams. Okay, So in the problem tells us, we have 0.9 kg of carbon dioxide for every kilogram of cement. So this is a conversion here 0.9 kg of carbon dioxide for every kilogram of cement. So we'll put that here. So for every one kg of cement, we have 0. kilograms of carbon dioxide. Okay, So let's just look at how our units cancel here, are metric tons, cancel our kilograms, cancel. So now we're in kilograms of carbon dioxide and we want moles of carbon dioxide. So we can convert this kilograms, two g by using our conversion in one kg there's 1000 grams. Okay, So our kilograms cancel. And now we're in grams of carbon dioxide but we want moles of carbon dioxide. So to go from grams of carbon dioxide, two moles of carbon dioxide. We need the molar mass of carbon dioxide and one mall of carbon dioxide there is The Molar mass is 44.01 g of carbon dioxide. Okay, So our grams cancel. And now we have the unit of moles of carbon dioxide, which is what we're looking for. So let's go ahead and solve So we know what our N is for our rearranged ideal gas law. We get 1.88 times to the 12th moles of carbon dioxide. Okay, So we have our moles. Our next thing is our our is our gas constant and this is a value. We should know this is 0.8 to Leaders times a T. M. Over more times kelvin t is temperature. And the problem, we're told we're going to assume that the ideal gas behaves at 1 80 M and 25 degrees Celsius. Our temperature is 25 degrees Celsius. But because our constant has temperature in kelvin, we need to convert this to kelvin and we do that by adding 273.15. So we have a temperature of 298. kelvin and then p they tell us is 1 80 M. Because we're assuming it behaves as an ideal gas under those conditions that they told us. So we have everything. We have N. We have our T and P. So all we need to do now is plug all of that in to solve for our volume of carbon dioxide emitted. So we have N Is 1. times 10 to the 12. No times are 0.08, Leaders times atmosphere over more times, kelvin times temperature. Our temperature is 298. Calvin. This is all over. P. RP is 1 80 M. Okay, so let's take a look at how our units cancel here because we're solving for volume, our unit that should be left over is leaders. Okay, so our moles cancel, Calvin, cancel a T. M cancel And look at their we're left with leader, which is perfect because we're solving for volume. So we get a volume a final volume of 4.60 times To the 13 leader. And this is going to be our final answer. This is the volume of carbon dioxide emitted by cement production in the us in 2021. That's the end of this problem. I hope this was helpful

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

Problem 101a

Chapter 10, Problem 101a

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.

Verified step by step guidance

Convert the temperature from Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \).

Use the ideal gas law equation: \( PV = nRT \), 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.

Calculate the number of moles of CO2 using the mass of CO2 produced (6 * 10^6 tons) and the molar mass of CO2 (44.01 g/mol). Convert tons to grams for this calculation.

Rearrange the ideal gas law to solve for volume: \( V = \frac{nRT}{P} \).

Substitute the values for \( n \), \( R \) (8.314 J/(mol·K)), \( T \), and \( P \) into the equation to find the volume of CO2.

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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 the behavior of gases under various conditions, making it essential for calculating the volume of gases like CO2 produced in combustion processes.

Greenhouse Gases

Greenhouse gases, such as carbon dioxide (CO2), trap heat in the Earth's atmosphere, contributing to the greenhouse effect and global warming. They are produced from various sources, including the combustion of fossil fuels in power plants. Understanding the role of these gases is crucial for addressing climate change and developing strategies for reducing emissions, such as carbon capture and storage.

Combustion of Fossil Fuels

The combustion of fossil fuels involves a chemical reaction between the fuel and oxygen, resulting in the release of energy, carbon dioxide, and other byproducts. This process is a primary source of energy for electricity generation but also significantly contributes to CO2 emissions. Recognizing the implications of fossil fuel combustion is vital for evaluating environmental impacts and exploring alternative energy sources.

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