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Problem 107 Hard Difficulty

Using the average atomic masses given inside the front cover of this text, calculate how many moles of each element the following masses represent.
a. 1.5 $\mathrm{mg}$ of chromium
b. $2.0 \times 10^{-3} \mathrm{g}$ of strontium
c. $4.84 \times 10^{4} \mathrm{g}$ of boron
d. $3.6 \times 10^{-6} \mu \mathrm{g}$ of californium
e. 1.0 ton $(2000 \text { lb) of iron }$
f. 20.4 g of barium
g. 62.8 g of cobalt

Answer

A.$2.9 \times 10^{-5} \mathrm{mol}$
B.$2.3 \times 10^{-5} \mathrm{mol}$
C.$4.48 \times 10^{3} \mathrm{mol}$
D.$1.4 \times 10^{-14} \mathrm{mol}$
E.$1.6 \times 10^{4} \mathrm{mol}$
F.0.148 $\mathrm{mol}$
G.1.065 $\mathrm{mol}$

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Video Transcript

Okay, so here we have a list of seven elements, seven elements and their masses, and we are going to find the number of moles within each of these masses. So to do that, we know that moles malls and is equivalent to mass divided by more mass. So that's what we're going to do all the way through their take each of the masses and divide them by the molar mass. That's just the atomic mass before I'm the product table. All right, let's get started. So 1st 1 here is chromium art, and we have points. Here's your 15 grams of chromium. So what we're gonna do is find out the product table and find its atomic maths happens to be 51 0.9 mine. Approximately grams per mole is a five. Yep. Sold. Induced. Take this mass. The bottom by the molar mass. And then what we get is a more so what we have here is 2.88 times tend to the exponents. They get a five most of chromium and instead of writing out times 10 to the exponents magnify. I just write e meaning times into the X one in Lincoln. Five moles. All right, so now we're just gonna plug in Chuck's remainder, basically. So here we have struck him. Strontium is a all quiet earth metal believe soaker too metal, if you can't find it. Us are. So it's, um molar masses, 87.62 grams per mole. It happened. Just divide. Nice nisi. That's a two. Okay, this potion is 2.28 times 10 to the exponents in the get of five moles. Uh huh. So quit. Small number. That's most next. Over here, we have boron. Okay, lets junk mass divided by Muller mouse. More massive born is 10 point eight 11 grams per mole. No, this is them equivalent to 4.47 No, actually, he's Oops. Well, I'm gonna write It is just 4000 actually. 476 most. It's a very large number, but we also did start off with four point. He also started basically for 40,000. It's next. We have California home. Mm. But here there's a catch. We are starting with micrograms. So we have to We must convert this to excuse me, grams for more. So you have to know Grampian toe convert to grams. Right? So let's just do a quick unit analysis. So you want to go to Gramps? So I'm just gonna see grams in the numerator. We're gonna multiply this basically by one. So, what is one gram equivalent to one pair, miss? Equivalent to one to the exponents. Six micrograms. So this is equivalent to one. And so we're basically not changing this number. The value of this quantity, you're just, you know, converting. So then we have micrograms in the you're more eager and to the memory of cancels out, we're left with Gramps. So we just multiply through and we yet our grams, that is sweet. Sickly, 3.63 times tend to exponents. Liftoff, gram. So extremely tiny number. But we must working, Gramps and I were going to take that mass. Let's go Another why? And then plugging joke grams weather by the molar mass of California. Mom, just Oh, change. And 51 151.0, 796 grams per mole. Right. So this quotient then, is one point 4330 times tend to the exponents. Negative. 14 moose. Right. Okay, Next we have iron and have a ton of which sounds like a lot, but it's okay. So now we have another unit analysis. All right, so we want to go to Gramps, so we're ready to find out what? When Graham is equivalent to right? So one gram is equivalent 1.10 times tend to the negative six turns. Yeah, tons of the numerator come ton in the denominator canceled felt, so just multiply through. Our product is 9000 700 184 0.7. Gramps, let's just quickly explain what I did because you didn't get so we have this unit here that we're trying to convert into Gramps what we do basically small supply this number by one. Okay, this is a well run toe. So we need a ton to be in the denominator or for to cancel out and for us to be left with Gramps in the new writer. Then we always whatever desired unit we want, it will be the numerator, and we just need to make sure that each quantity is equivalent to each other in this fraction in them. Also play through. Okay, That's what we did over here with iron. That's what we did over here with California. Okay? So I wouldn't take this mass and divide it by the molar mass of fire to find the malls in one ton of iron, which we can expect to be a lot because a 10 against you weighs a lot. All right, Grams. Okay. And the molar mass iron, 55 0.845 grams per mole. This thing accused us 16,000 294 0.60 0.689 most 16,000. So Yeah, she didn't see a lot. Next, we have, um, very, um 20.4 games for buryem supplied in chug. Most is equivalent to mask over Mullah Mask. Mullah Massoud. Barium is 1 37 0.372 grams per mole camps a new Mario Gangsters. You know, most of the denominator the denominator, which is the numerator. So we're left with moles on top, basically equivalent to 0.148 5.1485 Yes. Well, um last you have cobalt flooding. Jack Mass played by more mass is equivalent to most yourself. Don't like Mariza this point. The molar mass of Cobalt is with the 8.9 332 and this gives us basically around one a 10.65 moles. All right, we have it.

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