The matter in interstellar space consists almost entirely of hydr...

Question

The matter in interstellar space consists almost entirely of hydrogen atoms at a temperature of 100 K and a density of approximately 1 atom>cm3. What is the gas pressure in millimeters of mercury?

Accepted Answer

Hi everyone. This problem reads the air we breathe is composed of different gasses at near sea level, 288.15 kelvin. The density of air is approximately 2.7 times 10 to the 19th molecules per cubic centimeter, calculate the air pressure and millimeters of mercury. So our goal here is to calculate air pressure and millimeters of mercury. And because if we're dealing with gasses here, we're going to want to use our ideal gas law, which is pressure times volume, is equal to the number of moles times the gas constant R times temperature. And we're particularly interested in calculating pressure. So we need to isolate that variable by dividing both sides by volume. So we get pressure is equal to N R T over V. Okay, so let's go ahead and solve for what we don't have. So N represents moles. Okay, so we are given in the problem 2.7 times 10 to the 19th molecules per cubic centimeter. Okay, so our goal here is to go from molecules per cubic centimeter. We want to go from that to moles of air per leader. Alright, so let's go ahead and do that. So we want to first go from molecules to moles and we'll do that using avocados number. So in one mole of anything, There are 6.02, 2 times 10 to the 23 entities and in this case our entities is molecules Okay, so our molecules cancels and we're left with moles. So now we want to go from cubic centimeters to leaders and one leader, there is 1000 cubic centimeters. Okay, so that means n r number of moles is going to equal 0. Moles of air per leader. Alright, so we can make a note here and is equal to 0. 483 moles. Okay, so now R represents a gas constant 0.08206 leaders times atmosphere over more times Kelvin and T represents temperature. The temperature is 288.15 Kelvin. And pressure is given in. No we have everything we need to solve for pressure. Okay, so and we have our volume is equal to one leader. We're going to assume the one leader. Alright, so let's go ahead and plug in our values. So we get P is equal to N R T over V. So 0. moles times gas constant. R 0.8 to 06 leaders. Atmosphere over mole kelvin temperature is 288.15 kelvin. And this is over volume and our volume is one leader. Okay, So once we do this calculation we get pressure is equal to 1.06 atmospheres. But the question asks us for it in mm of mercury so we need to convert this. So 1.06 atmospheres. The conversion from atmospheres two millimeters of mercury is one atmosphere is equal to millimeters of mercury. Okay, So our units of atmosphere cancel, and our answer is millimeters of mercury. Alright, so we can go ahead and write pressure is equal to 806 mm of Mercury, and this is going to be the final answer. Okay, so this is the pressure, the air pressure and millimeters of mercury. That's it for this problem. I hope this was helpful.

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