On average, each person in the industrialized world is responsible for the emission of 10,000 kg of carbon dioxide (CO₂) every year. This includes CO₂ that you generate directly, by burning fossil fuels to operate your car or your furnace, as well as CO₂ generated on your behalf by electric generating stations and manufacturing plants. CO₂ is a greenhouse gas that contributes to global warming. If you were to store your yearly CO₂ emissions in a cube at STP, how long would each edge of the cube be?

Video transcript

Hello, fellow physicists today, we're to solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem, cows are a part of the livestock industry which contribute, contributes significantly to methane ch four emissions. According to studies, a cow produces 216 g of methane on average each day, since methane gas is a major greenhouse gas, there is ongoing research to find ways to reduce the amount of methane gas produced by cows. Suppose that a system has been developed to store the emitted methane. What would be the length of a cylinder with a radius, 1.00 m needed to contain the STP of muffly methane emissions of a cow assume each month has 30 days. Ok. So we're given some multiple choice answers. A is 9.6 centimeters. B is 85 centimeters C is 2.9 m and D is 3.6 m. So first off, we need to calculate the monthly methane emissions. A cow produces. So as given to us in the prom, a cow produces 216 grams of methane a day. And using dimensional analysis, we can find the monthly methane emissions. So let's do that multiplied by 30 days, as it visit says to assume each one has 30 days. So 30 days in one month. So when you plug that into a calculator, you should get 6408 grams per month. OK. So next, we need to convert the mass of methane gas into a volume using standard conditions of temperature and pressure, which is STP for short. So note that the molar mass for methane is 16.4 g per mole. So we'll write that down. So the molar mass which is gonna be denoted as capital M subscript C subscript four. So the molar mass of methane is 16.04 grams per mole. And then also we need to recall that the mole equation is N equals the mass divided by the molar mass. Awesome. So when we plug in our known values to determine the number of moles, the mass per month that we just the mass of methane produced by a cow each month, we determine the grams value to be 6408 grams per mole right or month. Well, we don't have to put the month down. We just need to know the grams amount divided by the molar mass which is 16.04 grams per mole. The grams cancel out giving us just moles. And when you plug that into a calculator, you should get 404 moles. So at this stage, we need to recall the ideal gas law, which the ideal gas law states that pressure multiplied by the volume is equal to the number of moles multiplied by the universal gas constant multiplied by the temperature. So when we rearrange this equation to solve the volume is we need to determine the volume of methane produced in a month. When you rearrange that you should get that the volume is equal to the number of moles multiplied by the universal gas constant, multiplied by the temperature all divided by the pressure. Awesome. So when we plug in our known variables to solve for V, let's do that. So there was 404 moles multiplied by the universal gas constant which the numerical value for that is 8.31 joules per mole multiplied by Kelvin multiplied by the temperature, which in this case, since we're dealing with STP, the standard temperature pre you know, for STP conditions, the standard temperature is 273 degrees or I should say 273 Kelvin. OK. And then the pressure which in this case, it's the atmospheric pressure, the numerical value for that is 1.013 multiplied by 10 to the fifth power pass scales. OK. So when you plug that into a calculator, the value for V that you should get is 9.05 m. Keep OK. So now we can begin to sol for the length of the cylinder. So let us recall the volume of a cylinder. So the volume of a cylinder is V equal to pi multiplied by the radius squared multiplied by the length. So we need to rearrange this equation to sulfur LVI. We're trying to find the length of the cylinder. So when we rearrange it, we should get that L equals the volume this divided by, yeah, now the volume divided by pi multiplied by the radius square. So now at this stage, we could plug in our known variables and note that in the prom, they gave the radius as 1.00 m. So let's plug in our known variables. The volume was 9.05 m cubed divided by pi and the radius was 1.00 M uses in meters square. So when you plug that into a calculator, you should get 2.9 m and that is our final answer. So that is the length of the cylinder needed to contain the STP for the monthly methane emissions of a cow. OK. So that means our final answer must be C 2.9 m. Thank you so much for watching. Hopefully, that helped and I can't wait to see you in the next video. Bye.