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Problem 109 Hard Difficulty

Using the average atomic masses given inside the front cover of this text, calculate the number of atoms present in each of the following samples.
a. 2.89 g of gold
b. 0.000259 mole of platinum
c. 0.000259 g of platinum
d. 2.0 lb of magnesium
e. 1.90 mL of liquid mercury (density $=13.6 \mathrm{g} / \mathrm{mL} )$
f. 4.30 moles of tungsten
g. 4.30 g of tungsten

Answer

A.$8.83 \times 10^{21}$
B.$1.56 \times 10^{20}$
C.$8.00 \times 10^{17}$
D.$2.25 \times 10^{25}$
E.$7.75 \times 10^{22}$
F.$2.59 \times 10^{24}$
G.$1.41 \times 10^{22}$

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Video Transcript

Okay, so here we have another list of seven elements and various quantities, never of them. And we are going to find the number of Adams of each element. So first off, we have gold and have 2.89 grams. So called. So first, let's just write some, um, equations don't. So, in order to find a number of Adams, um, let's just remind ourselves of that formula for a number of Adams. And because these are all elements, that's how we can use this equation. So we take malls basically and just multiply it by have a God Joe's constant the 6.2 to tempt in through the 23 number. So an aide candidates have a gorgeous constant. Right. Okay, But what if we don't have moles? But if you have mass, so we know that malls is equivalent to mass over molar mass, right? Okay. And I was these two formulas. I think you can do this. All right, let's first off by calculating the number of moles. So we take our mouths and divide by molar mass, which is here a capital M. So to find that we just look on our periodic table and find gold. Gold is in the sixth period. It's more mass is quite large. It's 196 0.2966 or EMS. Permal. Okay, all right. And that basically gives us zero 0.146 Yes, points. It's seven miles. So you know to find alums will take malls. I multiply it by avocado, just constant. So we take the 0.0 1467 multiply that by other guardians, constant on a. I could write it out because it's quite long and this gives us 8.8. You know, I'm going to write this in another color so it can stand out. North is in blue 8.8 35 or 36 for rounding times tend to the exponents 21 and here E is times 10 to the exponents 21. All right, let's move on. Me a couple, Marla, to go. Oh, and now we have platinum pt another group. Another period, six development. And they've already given us most. So we can just street plug in play in that formula, that number into this formula. So here we have it. Adams This is equivalent to malls multiplied by average car, just constant. So I'm just going toe. Scientific notation this number. So it's to temps 10 or 1234 It's a time center dates one that negative for, um multiplied by Abba. Gaja is constant and then we get one 0.55 Mine turns 10 to the exponents. 20 Adams of platinum. Next again, we have platinum, but 2.5 1910 to the negative four Gramps of it. So we have to take a longer with Okay, now that we understand how to use it, we can. Now I'm substitute moles into this equation to make it just one step quicker. So said over just writing doing this in two steps we can just straight away teeth or mass divided by Mullah Mass, which is moves multiply this by regardless constant right where we go. And that's what we're gonna use to light Adams. Just make it go, but more quicker. So we take our mass 2.59 divided by the molar mass of Putman, which is 1 95 Where's promote and then multiply this by avocados number right. This then equals seven point mine. Mine, Mine, Mine five times tend to the exponents. 17% time tend to the 17 Up. Next, we have £2 of like a museum. It's time to do so, units. Conversions. The way were you will do. That is you wanna goto grams? We must Dakota Grams his work gonna work with more mass. And that's and grand. So we need to multiply this number by quantity by one, basically. So what is the equivalent? One ground? Because whatever to pull the torn ground will yield this bracket to be one. So we don't change this quantity over here. These £2. All right, so we know that when graham is 2.2 times 10 to the negative three pounds quite learn traction. Yes. Tucked into trade. £3 which then equals 907 0.185 grams. Quite a lot. Yeah, and then we'll use this. Same for them. Over here. Find number of atoms with magnesium. Okay, so we take my 107.185 grams. Divide it. Buzim Lemus of magnesium, which is like 24 24.3 grams per moon, then all multiplied by have a guard Joe's constant to equal 2.24 times tend to the exponents 25 Adams. Next, we have mercury just like the Onley look with metal of it. So now, because the liquid repair work in volumes. Middle leaders here. But we saw him Gramps for part of this. So but we have to do now is to use density and home where we have volume density will help us convert to grams to mass density is mass toilet by bombing for it. So we've been told that the density of, um mercury is one point through is 13.6 grams per mil a leader. So, yes, it just happens toe workout and we that's favorable. But what we want is from Millie or she can't a lot. So must be in the bottom. And grams was beyond topcoats. What we want to isolate for some middle leaders wants a low. And then we get Gramps. So then, if you multiply through, we get a mass 25 go, that could be better. 25 0.84 Um, Gramps. All right, so now we're still looking for Adams or to use the same Yeah, formula as above take mass divided by molar mass of mercury Just like 200.59 grams per mole. Multiply that by of a guard just constant and a And this comes up to being seven 0.7 five times turned to the exponents 22. Look, there we have it. Next up is tungsten w Okay. And we've looked We've been given malls. Sorry. Just multiply the those moles by of a guy Just constant came. Multiply those moles. But I got yours, Constant. Oops to find number abs. Correct. So you have 4.3 moles. What is happening? 4.3 moles multiplied by average Rogers constant 6.22 times 10 to 23 perm ALS is it so? Yes, which then gives us 2.58 nine times 10 to the exponents. 24 Adam sometimes too. Lastly, you have now 4.3 grabs tungsten. How just the formula that we derived and take mass divided by the molar s of tungsten, which is 183 0.84 grams per mole. Then multiply this. But I have a gorgeous constant and we get one No one just blue, please. For the last one we get 1.48 point 408 times 10 to the exponents, 22 Adams of tungsten.

McMaster University
Top Chemistry 101 Educators
Stephanie C.

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