Modern pennies are composed of zinc coated with copper. A student determines the mass of a penny to be 2.482 g and then makes several scratches in the copper coating (to expose the underlying zinc). The student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the HCl (the copper remains undissolved): Zn(s) + 2 HCl(aq)¡ H2( g) + ZnCl2(aq) The student collects the hydrogen produced over water at 25 °C. The collected gas occupies a volume of 0.899 L at a total pressure of 791 mmHg. Calculate the percent zinc (by mass) in the penny. (Assume that all the Zn in the penny dissolves.)

Video transcript

Hey there. Welcome back. Alright. So, when acquaints, hydrochloric acid is added to metallic zinc, small quantities of hydrogen gas are produced and we can see that through this equation. Now, we are probably going to be using this equation. So let's go ahead and make sure that this is a balanced equation by taking a look at it. It looks like it is. So, we're all good. All right. So, the hydrogen gas produced. So, we're talking about this gas right here from this direction is collected and bubbled through water. The gas then becomes saturated with water vapor, so realize that it is no longer just reached to gas. It is H two gas plus um H +20 gas, right? Water vapor the gas collected occupies a volume of millimeters at 50 degrees Celsius With a total pressure of 1.025 atmospheres. What is the partial pressure of hydrogen gas? And then we have another question here determine the mass of zinc. So, we also want the massive zinc here That must have been reacted to produce this amount of hydrogen. We have water pressure vapor pressure of water at 50°C as 92.6 tours. All right, so, let's go ahead and look at the first question here where they just want the partial pressure of hydrogen gas here. So, the pressure that is given is total pressure. So, it's going to be the pressure of H2 and the pressure of water. Right, So the total pressure That's given is going to be pressure of H2 Plus pressure of H 20. Right, So we actually have the pressure reached to have given to us at that same temperature. Um and we have the total pressure. So we can actually figure out the pressure of hydrogen gas by just subtracting the pressure of water from the total. Right? Soapy of H two is going to equal to. So the total is 1.025 atmospheres - Well, here we have that in tours. So let's go ahead and take this 92.6 tours and convert that into atmospheres. Right, because we can't subtract tours from atmospheres. So the conversion factor for that is in one atmosphere There is 760 tours. Right? So this cancels out the tour. And that will give us .1 - 1 Atmospheres. There we go. So that's the pressure of water. So minus .1- Atmospheres. So that's H 20. And that's total. And that will give us partial pressure of hydrogen as 0.90 32. Alright, so that is the answer to the first question that they had. Alright, so done with that. Let's go ahead and take a look at the second one. The second one, they want the mass of zinc. Alright, so, We obviously the only information that we have is information on hydrogen gas and we don't have grams or moles of H2. What we have here is pressure vote to we have the volume that it takes up and add the temperature that it's at. So we're actually going to need to utilize the ideal gas law equation PV equals Nrt Okay. And we're going to actually solve for n for the moles of gas of each two and then once we have the moles of that, we can do a multiple comparison and find the molds of end of zinc and then obviously just convert those molds of zinc into grams because they want um let's see. They want math. So most likely grams. Right? So let's go ahead and rearrange ideal gas law equation to find to software and so it's going to be PV divisible sides by R. T. There we go. So p we already have an atmosphere. So let's go ahead and plug that in point 90 Volume is given to us. It is 320 ml. So we actually need leaders. So go ahead and divide that value by 1000 to convert into leaders. And that will be a .32 L. Right? And then divided by R. T. So R is the gas constant. We always have that .08 206. Leaders times atmospheres over mold time Calvin. And then temperature here has to be in Calvin's as well because we do have Calvin in the gas unit in the Gas constant. So it has to match and we do have 50°C here as our temperature that's given to us. So in order to convert that to Calvin, we add to 73.15 to that. Okay. And that will give us 323.15 Calvin. So that's the temperature that we plug into this equation .15. Because if you used 50°C, you will get a completely different answer. All right, so here we can cancel out the atmosphere so we can cancel out the leaders and the calvins. Right? So that's why it's important to use um correct units because otherwise they're not going to cancel out and you're not going to get the right answer. So here we have moles leftover. So end here and that's the end of of each two that we're solving for here. So that answer will be .0109. Alright, so now that we have moles of H two, we can use storage geometry using that balanced equation. That was given to us to find the molds of zinc. Alright, so this is like two A or to point B part per B, part B of the second step or the second question here. Alright, so now we're going to take point oh one oh nine moles of each two. That's given to us and we're going to do a multiple comparison. We're going to put moles of H two on the bottom because we are not interested in that we want that to cancel out. But we do want information on the sink. So we're gonna put molds of zinc on top. So, by looking at the balanced equation, we can see that it's just a 1 to 1 mole ratio. It's so one think of mole being used to produce one. Think of hydrogen gas of H two uses just 1 to 1. So that doesn't change the moles. And now we can go ahead and convert zinc into grams. So we're going to put zinc of molds of zinc on the bottom because we want that to cancel out now and then one mole of zinc. If you take a look at the product team, we will see that it weighs 65.38 g. Alright, so that canceled out. And our final answer for the second part here is going to be . grams of the sink. Right? So that's our second answer here. Alright, so, we've got everything. We found the partial pressure of H two by subtracting the vapor pressure of water from the total. And then for the second question, we needed to find moles of H two. First by using the ideal gas law before we could use those moles and convert into molds of zinc and then convert into grams or mass of zinc. All right, thank you so much for watching and we'll see in the next video