Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H₂). The number density is about 1 atom/cm³ and the temperature is about 3 K. a. Estimate the pressure in interstellar space. Give your answer in Pa and in atm.

Video transcript

Hey, everyone. Let's go through this practice problem. In the outer reaches of our solar system. A cloud of hydrogen gas is formed, the cloud has a density of one atom per two cubic centimeters and a temperature of negative 271 degrees Celsius. What is the pressure inside this cloud? Assume hydrogen gas behaves like an ideal gass. Option A 1.3 multiplied by 10 to the power of negative pascals. Option B 1.5 multiplied by 10 to the power of negative pascals. Option C 1.3 multiplied by 10 to the power of negative pascals and option D 1.5 multiplied by 10 to the power of negative 12 pascals. Fortunately, for us, this is a fairly simple problem. As long as you remember the ideal gas law, which states in some forms that the pressure multiplied by the volume of the gas is equal to the number of particles. In this case, atoms multiplied by the Boltzmann constant multiplied by the temperature of the gas. We're looking for the pressure of the gas cloud. So let's solve this formula for P pressure by dividing both sides of the equation by V. So the number of particles divided by the volume multiplied by the Boltzmann constant multiplied by the temperature is what the pressure of the cloud is. We're given the temperature, the Boltzmann constant is basically a given and we're given the number of atoms per vol for per unit volume. So really the problem at this point is simply a matter of plugging in the variables that we have. So for n we're told one atom per volume of 2.0 cubic centimeters. So 2.0 cubic centimeters and we want to convert this into cubic meters. So remember the conversion for that is one m or centimeters and cube, the whole thing in order for it to be a good unit conversion, then multiplied by the Boltzmann constant or 1.38, multiplied by 10, the power of negative 23 Jews per Calvin and then multiply by the temperature. And real quick, I want to throw out on the side what that temperature is because we're given the temperature as negative 271 degrees Celsius. But the ideal gas law only works if the temperature is in Kelvins. So we'll want to take the temperature in Celsius 207 negative 271 degrees Celsius and add 273.15. And that will give us the temperature in Kelvins. So doing the math on that, we find a temperature of about 2.15 Kelvins. So that's what we'll put in for temperature in our formula. And if we put all this into a calculator, we find a pressure of approximately 1. multiplied by 10, raised to the power of a negative 17 pascals. So that is the answer to our problem. And if you look at our multiple choice options, this agrees with option B. So option B is the correct answer to the problem and that is it for this problem. I hope this video helped you out. If you need more practice, please consider checking out our other tutoring videos which will give you more experience with these types of problems. But that's all for now. I hope you all have a lovely day. Bye bye.