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The vapor pressure of mercury is $0.0020 \mathrm{mmHg}$ at $26^{\circ} \mathrm{C} .$ (a) Calculate $K_{c}$ and $K_{P}$ for the process $\mathrm{Hg}(l) \rightleftharpoons \mathrm{Hg}(g) .$ (b) $\mathrm{A}$ chemist breaks a thermometer and spills mercury onto the floor of a laboratory measuring 6.1 m long, 5.3 m wide, and 3.1 m high. Calculate the mass of mercury (in grams) vaporized at equilibrium and the concentration of mercury vapor in $\mathrm{mg} / \mathrm{m}^{3} .$ Does this concentration exceed the safety limit of $0.05 \mathrm{mg} / \mathrm{m}^{3} ?$ (Ignore the volume of furniture and other objects in the laboratory.)

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(a) $K_{p}=2.6 \times 10^{-6}, K_{c}=1.1 \times 10^{-7}$(b) $2.1 \mathrm{g}, 21 \mathrm{mg} / \mathrm{m}^{3},$ above safety limit

Chemistry 102

Chapter 14

Chemical Equilibrium

Carleton College

Drexel University

University of Toronto

Lectures

10:03

In thermodynamics, a state of thermodynamic equilibrium is a state in which a system is in thermal equilibrium with its surroundings. A system in thermodynamic equilibrium is in thermal equilibrium, mechanical equilibrium, electrical equilibrium, and chemical equilibrium. A system is in equilibrium when it is in thermal equilibrium with its surroundings.

00:54

In chemistry, chemical equilibrium (also known as dynamic equilibrium) is a state of chemical stability in which the concentrations of the chemical substances do not change in the course of time due to their reaction with each other in a closed system. Chemical equilibrium is an example of dynamic equilibrium, a thermodynamic concept.

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The vapor pressure of merc…

05:23

A student breaks a thermom…

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Mercury is a poison, and i…

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Mercury and many of its co…

So for this problem, we're looking at the equilibrium between liquid mercury and gaseous mercury. So first you want to find the KP, which is actually easy because we know that for K p, which is equal Berm constant taking into account partial pressure on Lee taking to account gaseous substances. And we only have one, and we were given that it is equivalent to 0.2 But this is not an A t m like we would want it to be so we can convert a team. And once we convert to a T. M, you get 2.6 times 10 to the negative six e t. M as her KP value and therefore our Casey value. We're going to use this area. This equation KP equals K C are tee next to the difference of moles. So if we rearrange this, we know we know it cape he is. It is. I just use this version. It might be a little bit easier to see the writing out whole thing over are we know ideal gas constant 0.0 8 to 1 the temperature. We were told that this is at 26 degrees Celsius, so 26 degrees Celsius. Adding the 2 73 to avert to Calvin is to 99 degrees Calvin. And since we only have one mole of gaseous substance in our product side and none in our reactive side, you raise this just to a power of one which is just itself. So you don't have to include that and we find that the Casey value is 1.1 times 10 to the negative seven. So now, looking at B, we're looking at the spill. But the first thing you want to dio is find the volume of the lab. Since we're giving the dimensions of the lab, we can go ahead and multiply them all together to find volume, just like we would find the volume of any other object. And this comes out to be 100 meters cubed, and it's important to remember the K C is going to be equal to just the concentration of mercury. And that's our product for mercury because it's gaseous and for equal of room constants that take into account concentration. We only talk about gaseous and Equus substances. So since we know that we're gonna need to do a conversion. And that is our concentration. We want to cover two moles. So wait, So this means at this point we've crossed out moles. Oops with the times. Yes. We have to keep going. The one leader on top crosses out this. And since we're gonna want meters Cube, you know, one leader is equivalent to 1000 centimeters. Cute. They were going to do one centimeter over 0.1 meters. All this cubed is equivalent. First, we have to times it by the volume of the lab. Before we can do what it is we want to, we find that it is equivalent to 2.2 grams. We're not done. However, to find the concentration Ah, hydrogen mean of mercury. We need to dio mass. We found over the total volume of the lab that we calculated earlier. And this is equivalent to zero point 0 to 2 crams per year Cube. But in order for us to compare it directly to what are safe level is that was given in the problem. You want this in milligrams so you can easily convert two milligrams, get 22 milligrams per meter cubed. And since this value is 22 does greatly exceed the safe value that was set in the problem itself.

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