A plasma-screen TV contains thousands of tiny cells filled
with a...

Question

A plasma-screen TV contains thousands of tiny cells filled
with a mixture of Xe, Ne, and He gases that emits light of
specific wavelengths when a voltage is applied. A particular
plasma cell, 0.900 mm * 0.300 mm * 10.0 mm, contains
4% Xe in a 1:1 Ne:He mixture at a total pressure of 66.66 kPa.
Calculate the number of Ne atoms in the cell and
state the assumptions you need to make in your calculation.

Accepted Answer

Hey everyone in this example, we have a fluorescent tube with the length four ft and a diameter of 1.5 inches containing mercury vapor and argon. We're told that a specific fluorescent bulb contains point to 63% mercury and has a total pressure equal to 304 paschal's inside the lamp. We need to figure out how many mercury atoms are present in the lamp and state all assumptions made. So that first piece of information, they give us point to 63% of mercury. We should recognize this as our mole percent. We want to go ahead and convert this to a mole fraction. So we would say that our mole fraction of mercury is equal to point to 63, sorry .263 Divided by 100, which is equal to a value of 2.63 times 10 to the negative third power for mercury. Next, we want to go ahead and recall our formula for total pressure. So pit and that's going to equal to the pressure of our gas, which is our mercury vapor. And this is then multiplied by the molds of our gas. And we want to utilize this formula because ultimately we're going to use our ideal gas law PV equals Nrt to ultimately answer this question to find our atoms of mercury by converting from molds of mercury to atoms. So what we want to do is using this formula, we're going to reformulate it because we want to find our pressure of our gas in order to use our ideal gas constant. So we would say that our pressure of our gas is equal to our molds of our mercury Multiplied by the total pressure, which is what we're given in this question. And so we would say that our pressure of our mercury gas is equal to our moles of our gas, which we said the mole fraction for mercury is 2.63 times 10 to the negative third power above. And then our total pressure for the inside of our flash lamp is given to us as 304 paschal's. So we're going to plug that in times 304 paschal's and this quantity or this product here is going to give us a value equal to 0.800 paschal's. And so ultimately, as we said earlier, we want to find the moles of our mercury gas to ultimately then get to our atoms of mercury. And so we want to utilize what we recall as our ideal gas law, P. V pressure times volume is equal to the molds of our gas times the ideal gas constant R times the temperature in kelvin. And we would go ahead and reformulate this to solve for moles of mercury and equal to the pressure of our gas, multiplied by its volume and then divided by our ideal gas constant R times the temperature in kelvin. Now, out of all the work we've done so far. The only assumption we've made is for our mole fraction here. So we can also go ahead and write that out as our first assumption, since the question wants us to keep track of that now, right now we do have the pressure of our mercury gas, but we have it in units in pascal's here and we want for our ideal gas law pressure to be in units of A T. M. So we should recall that pressure should be equal to a. T. M's for our ideal gas law. And so therefore we're going to make a conversion factor where we're going to take our 0.800 paschal's As our pressure. And we're going to recall that we have in one ATM 101 or 101, paschal's. And so this allows us to cancel out our units of paschal's leaving us with a T M's for pressure, which is what we want for ideal gas law. And this is going to give us a value equal to 7.8906 times 10 to the negative six power A. T. M's for our pressure. And actually we should correct this so that it's 7. 56 times 10 to the negative six power A T M's for our pressure of mercury. So we also should recognize in our ideal gas equation, we utilize volume. We're not given any information in the prompt for our volume of our gas. So we're going to have to calculate that by recalling our formula for volume. And so I'm just going to make a division here and continue on the right hand side. So we would recall that our formula for the volume specifically the volume of a cylinder because we're dealing with the lamp here or a tube light. Rather this is going to equal the following formula where we take pi times our radius squared and then multiplied by our height of our tube light. Now looking back at the prompt, they give us a diameter so that's equal to 1.5 inches. And we're going to take this diameter divided by two and convert from inches into centimeters for our radius. So we should go ahead and let's do that below here. What we would have is that our radius is equal to our given diameter 1. in we're going to divide this by two and then we're going to multiply this quantity by a conversion factor. Where we're going to go from inches to centimeters. So we should recall that we have in one inch 2. centimeters. And so this allows us to cancel out our units of inches, leaving us with centimeters as our final unit for radius. And what we're going to get for our radius is a value of 1. centimeters. And so our next step is to make sure we have the proper height for our formula for the volume of our cylinder of our tube light. And what we should recognize is that the prompt gives us a height. But in feet we want to convert this also two centimeters. So utilizing that information, we're going to have our four ft and we're going to multiply by our first conversion factor to go from feet to inches. And then from inches we want to go into centimeters. So we should recall that In one ft we have 12" and we should recall our next conversion factor that we use before. Where for one inch we have 2.54 cm. I'm sorry, this is cm here. And so now we're able to cancel our units of inches as well as feet leaving us with centimeters for our height. And this is going to give us a height value equal to 1 21. centimeters for our to blight. And so now we can find the volume of our to blight Which is a cylinder still equal to pi multiplied by our radius which above we said is 1.905 cm which is squared and then multiplied by a value for height which above we found in cm as 121.92 cm. And this is going to give us a value of 1390 cubic centimeters when we multiply our centimeters squared times another unit of centimeters. So we should recall that one cc is equal to one millimeter. And because we want our final volume for our tube light to be in units of leaders. We're going to convert from milliliters to leaders. So we're going to take our cubic centimeters 1390 cubic centimeters. But instead of writing it as cubic centimeters because we know that it's equal to one millimeter, we can go ahead and write 1390 mL and focus on converting from milliliters to liters by recalling that we have in one leader 10 to the third power milliliters because our prefix milli gives us 10 to the three. And so now we can go ahead and cancel out middle leaders leaving us with leaders as our volume for tube light. And this is going to give us a value equal to 1. leaders. And now moving on to our second assumption based on us having our volume in the proper units as well as our pressure on the proper units. We should recognize that temperature is also involved in our ideal gas equation. So we're going to assume that we have standard temperature As our 2nd assumption. And so now we can find our moles of our mercury gas equal to our pressure of our mercury, which we said is equal to in a T. M's 7.8956 times 10 to the negative six power A T. M's. This is then multiplied by our volume, which we found as 1.39 liters and then divided by our ideal gas constant, which we should recall is equal to 0.8206 Leaders times A t. M's divided by moles times kelvin. And then we're going to plug in. Our assumption for standard temperature, which we would assume is 298.15 Kelvin. So this is our assumption here. And so before we calculate our final answer, we're going to cancel out our units. We can get rid of a T. M's. We can get rid of leaders. We can also cancel out kelvin, leaving us with our final unit as molds for our moles of mercury, which is what we want. And when we take the value of this entire quotient in our calculators, we're going to get a result equal to 4.4857 times 10. And I'm just gonna scoot this over. So we have enough room times 10 to the negative seventh power And this is in units of moles of mercury. So this is our moles of our gas. And so finally having moles of our gas mercury, we can find our atoms of mercury by using avocados number. So we'll say that our mercury atoms are equal to our current moles of our gas mercury. So we have that as 4.4857 times 10 to the negative seven power moles. And we're going to recall the conversion factor that for one mole of mercury, we have avocados number, which we recall is six point oh 22 times 10 to the 23rd power mercury atoms. And so this allows us to cancel out moles of mercury with moles of mercury leaving us with mercury atoms, which is what we want. And for our final result to complete this example, we get a result equal to 2.70 times 10 to the positive 17th power mercury atoms. And this is going to complete this example as our final answer for the number of mercury atoms present in our fluorescent lightbulb or to blight. So this is our final answer. To complete this example. I hope that everything I reviewed was clear. But if you have any questions, please leave them down below and I will see everyone in the next practice video.

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