Question

A closed container has 4.02 ⋅ 10^23 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10^−24 grams. Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container?

1) 6.71 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134
2) 5.69 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69
3) 0.67 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134 ⋅ 10^−1
4) 0.57 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69 ⋅ 10^−1
could you please explain how you got there? I want to learn!

Answer 1

First if each atoms is X, and each X weighs Y grams

the total weight would be

Atom 1 2 3 4 5 ..... X Total Number Atoms
Grams Y+Y+Y+Y+Y ...... +Y+Y+Y Total Mass

Instead of adding all of Atoms weight, it would be easier to multiply X times Y.

Knowing this which two equations can be eliminated?

1) 6.71 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134
2) 5.69 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69
3) 0.67 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134 ⋅ 10^−1
4) 0.57 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69 ⋅ 10^−1

Answer 2

I'm not sure

Answer 3

2 and 4?

Answer 4

Which answers is using adding atoms to weight and which is multiplying atoms and weight?

4.02 ⋅ 10^23 atoms atom of the gas weighs 1.67 ⋅ 10^−24 grams

1) 6.71 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134
2) 5.69 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69
3) 0.67 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134 ⋅ 10^−1
4) 0.57 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69 ⋅ 10^−1

Answer 5

1 and 3 are multiplying, and 2 and 4 are adding

Answer 6

Yes 2 and 4. I didn't see your second reply

Answer 7

okay, what do I do next?

Answer 8

1 and 3 are multiplying

Answer 9

So that means 2 and 4 are already wrong, so that leaves us with ....

1) 6.71 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134

3) 0.67 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134 ⋅ 10^−1

Now it gets a bit more complicated.

Answer 10

okay, what next :)

Answer 11

What is the difference in the answers? I'm NOT talking about subtraction.

1) 6.71 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134
3) 0.67 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134 ⋅ 10^−1

Just look at the first numbers before the grams.

Answer 12

1, has a whole number, and 3, doesn't.

Answer 13

at the end, of 3, there is a scientific notation

Answer 14

All good answers, but not the answer I am looking for.

1) 6.71 grams
3) 0.67 grams

Answer 15

I don't know then

Answer 16

This might help you see it better ....

All good answers, but not the answer I am looking for.

1) 6.710 grams
3) 0.671 grams

Answer 17

1 has a decimal after the 6, whereas 3 has a decimal before the 6

Answer 18

Yes

Answer 19

Now which one is correct?

1) 6.71 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134
3) 0.67 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134 ⋅ 10^−1

Look at the scientific notation one is 10^23 and the other is 10^-24

Correct?

Answer 20

3?

Answer 21

You didn't answer my question.

Answer 22

Look at the scientific notation one is 10^23 and the other is 10^-24

Correct?

Answer 23

originally yes.

Answer 24

Yes

if you multiply 10^23 and 10^-24

You get 10^-1

SO THREE is CORRECT

Answer 25

Yay! I can be taught! Thank you so much!

Answer 26

Hang in there cat!