Math / Numbers & Operations

QuestionA thimble of water contains $4.0 \times 10^{21}$ molecules. The number of moles of $\mathrm{H}_{2} \mathrm{O}$ is $6.6 \times 10^{-3}$ $6.6 \times 10^{-23}$ $2.4 \times 10^{23}$ $2.4 \times 10^{-23}$ $2.4 \times 10^{45}$

Studdy Solution

STEP 1

What is this asking? How many moles of water are there in a thimble if the thimble contains $4.0 \times 10^{21}$ molecules of water? Watch out! Remember Avogadro's number and what it represents!
Don't mix up molecules and moles!

STEP 2

1. Recall Avogadro's Number
2. Calculate the Number of Moles

STEP 3

Avogadro's number, $N_A$ , tells us how many particles (like molecules) are in one mole of a substance.
It's a huge number, approximately $6.022 \times 10^{23}$ particles per mole.
So, if we have one mole of water, we have $6.022 \times 10^{23}$ molecules of water.
Got it?
Super important!

STEP 4

We're given that our thimble has $4.0 \times 10^{21}$ molecules of water.
We want to figure out how many moles this is.
Think of it like this: if Avogadro's number tells us how many molecules are in one mole, we can use it to figure out how many moles we have given a certain number of molecules.

STEP 5

To do this, we'll divide the number of molecules we have by Avogadro's number.
This is like asking, "How many groups of $6.022 \times 10^{23}$ molecules fit into $4.0 \times 10^{21}$ molecules?" The answer will give us the number of moles.

STEP 6

Let's set up the calculation: $\text{Number of Moles} = \frac{\text{Number of Molecules}}{N_A}$

STEP 7

Plug in the values: $\text{Number of Moles} = \frac{4.0 \times 10^{21}}{6.022 \times 10^{23}}$

STEP 8

Now, let's crunch the numbers: $\text{Number of Moles} \approx \frac{4.0}{6.022} \times 10^{21-23}$ $\text{Number of Moles} \approx 0.664 \times 10^{-2}$

STEP 9

We can rewrite this in scientific notation as: $\text{Number of Moles} \approx 6.64 \times 10^{-3}$ So, our thimble of water contains approximately $6.6 \times 10^{-3}$ moles.
Awesome!

STEP 10

The thimble contains approximately $6.6 \times 10^{-3}$ moles of water.

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QuestionA thimble of water contains $4.0 \times 10^{21}$ molecules. The number of moles of $\mathrm{H}_{2} \mathrm{O}$ is $6.6 \times 10^{-3}$ $6.6 \times 10^{-23}$ $2.4 \times 10^{23}$ $2.4 \times 10^{-23}$ $2.4 \times 10^{45}$

Studdy Solution

STEP 1

What is this asking? How many moles of water are there in a thimble if the thimble contains $4.0 \times 10^{21}$ molecules of water? Watch out! Remember Avogadro's number and what it represents!
Don't mix up molecules and moles!

STEP 2

1. Recall Avogadro's Number
2. Calculate the Number of Moles

STEP 3

Avogadro's number, $N_A$ , tells us how many particles (like molecules) are in one mole of a substance.
It's a huge number, approximately $6.022 \times 10^{23}$ particles per mole.
So, if we have one mole of water, we have $6.022 \times 10^{23}$ molecules of water.
Got it?
Super important!

STEP 4

We're given that our thimble has $4.0 \times 10^{21}$ molecules of water.
We want to figure out how many moles this is.
Think of it like this: if Avogadro's number tells us how many molecules are in one mole, we can use it to figure out how many moles we have given a certain number of molecules.

STEP 5

To do this, we'll divide the number of molecules we have by Avogadro's number.
This is like asking, "How many groups of $6.022 \times 10^{23}$ molecules fit into $4.0 \times 10^{21}$ molecules?" The answer will give us the number of moles.

STEP 6

Let's set up the calculation: $\text{Number of Moles} = \frac{\text{Number of Molecules}}{N_A}$

STEP 7

Plug in the values: $\text{Number of Moles} = \frac{4.0 \times 10^{21}}{6.022 \times 10^{23}}$

STEP 8

Now, let's crunch the numbers: $\text{Number of Moles} \approx \frac{4.0}{6.022} \times 10^{21-23}$ $\text{Number of Moles} \approx 0.664 \times 10^{-2}$

STEP 9

We can rewrite this in scientific notation as: $\text{Number of Moles} \approx 6.64 \times 10^{-3}$ So, our thimble of water contains approximately $6.6 \times 10^{-3}$ moles.
Awesome!

STEP 10

The thimble contains approximately $6.6 \times 10^{-3}$ moles of water.

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Studdy Solution

STEP 1

What is this asking? How many moles of water are there in a thimble if the thimble contains 4.0×10214.0 \times 10^{21}4.0×1021 molecules of water? Watch out! Remember Avogadro's number and what it represents!Don't mix up molecules and moles!

STEP 2

1. Recall Avogadro's Number2. Calculate the Number of Moles

STEP 3

STEP 4

STEP 5

To do this, we'll **divide** the number of molecules we have by Avogadro's number.This is like asking, "How many groups of 6.022×10236.022 \times 10^{23}6.022×1023 molecules fit into 4.0×10214.0 \times 10^{21}4.0×1021 molecules?" The answer will give us the number of moles.

STEP 6

Let's set up the calculation: Number of Moles=Number of MoleculesNA\text{Number of Moles} = \frac{\text{Number of Molecules}}{N_A}Number of Moles=NA​Number of Molecules​

STEP 7

**Plug in the values:** Number of Moles=4.0×10216.022×1023\text{Number of Moles} = \frac{4.0 \times 10^{21}}{6.022 \times 10^{23}}Number of Moles=6.022×10234.0×1021​

STEP 8

Now, let's **crunch the numbers**: Number of Moles≈4.06.022×1021−23\text{Number of Moles} \approx \frac{4.0}{6.022} \times 10^{21-23}Number of Moles≈6.0224.0​×1021−23 Number of Moles≈0.664×10−2\text{Number of Moles} \approx 0.664 \times 10^{-2}Number of Moles≈0.664×10−2

STEP 9

We can rewrite this in scientific notation as: Number of Moles≈6.64×10−3\text{Number of Moles} \approx 6.64 \times 10^{-3}Number of Moles≈6.64×10−3 So, our thimble of water contains approximately 6.6×10−36.6 \times 10^{-3}6.6×10−3 moles.Awesome!

STEP 10

The thimble contains approximately 6.6×10−36.6 \times 10^{-3}6.6×10−3 moles of water.

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What is this asking? How many moles of water are there in a thimble if the thimble contains $4.0 \times 10^{21}$ molecules of water? Watch out! Remember Avogadro's number and what it represents!
Don't mix up molecules and moles!

1. Recall Avogadro's Number
2. Calculate the Number of Moles

To do this, we'll divide the number of molecules we have by Avogadro's number.
This is like asking, "How many groups of $6.022 \times 10^{23}$ molecules fit into $4.0 \times 10^{21}$ molecules?" The answer will give us the number of moles.

Let's set up the calculation: $\text{Number of Moles} = \frac{\text{Number of Molecules}}{N_A}$

Plug in the values: $\text{Number of Moles} = \frac{4.0 \times 10^{21}}{6.022 \times 10^{23}}$

Now, let's crunch the numbers: $\text{Number of Moles} \approx \frac{4.0}{6.022} \times 10^{21-23}$ $\text{Number of Moles} \approx 0.664 \times 10^{-2}$

We can rewrite this in scientific notation as: $\text{Number of Moles} \approx 6.64 \times 10^{-3}$ So, our thimble of water contains approximately $6.6 \times 10^{-3}$ moles.
Awesome!

The thimble contains approximately $6.6 \times 10^{-3}$ moles of water.