name
molar conversion practice
show all your work and circle your final answer!!!!
sig fig rules: your final answer has the same number of sig figs as the given.
1. how many molecules are there in 6.82 grams of n₂?

2. how many moles are in 52.0 grams of nh₃?

3. how many grams of hydrogen are in 9.37 x 10²³ molecules of ammonium sulfate?

4. how many moles of oxygen are in 4.88 moles of iron iii hydroxide?

5. how many molecules are in 5.30 moles of calcium phosphate?

Question

name
molar conversion practice
show all your work and circle your final answer!!!!
sig fig rules: your final answer has the same number of sig figs as the given.
1. how many molecules are there in 6.82 grams of n₂?

2. how many moles are in 52.0 grams of nh₃?

3. how many grams of hydrogen are in 9.37 x 10²³ molecules of ammonium sulfate?

4. how many moles of oxygen are in 4.88 moles of iron iii hydroxide?

5. how many molecules are in 5.30 moles of calcium phosphate?

Accepted Answer

### Question 1: How many molecules are there in 6.82 grams of $ \text{N}_2 $?

# Explanation:
## Step 1: Calculate the molar mass of $ \text{N}_2 $
The molar mass of $ \text{N} $ is $ 14.01 \, \text{g/mol} $, so for $ \text{N}_2 $:
$ \text{Molar Mass of } \text{N}_2 = 2 \times 14.01 \, \text{g/mol} = 28.02 \, \text{g/mol} $

## Step 2: Convert grams to moles
Use the formula $ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} $:
$ \text{Moles of } \text{N}_2 = \frac{6.82 \, \text{g}}{28.02 \, \text{g/mol}} \approx 0.2434 \, \text{mol} $

## Step 3: Convert moles to molecules (using Avogadro’s number $ 6.022 \times 10^{23} \, \text{molecules/mol} $)
$ \text{Molecules} = \text{Moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} $
$ \text{Molecules} = 0.2434 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.466 \times 10^{23} \, \text{molecules} $

## Step 4: Apply significant figures (3 sig figs, same as 6.82)
$ \text{Final Answer} \approx 1.47 \times 10^{23} \, \text{molecules} $

# Answer:
$ \boxed{1.47 \times 10^{23} \text{ molecules}} $

### Question 2: How many moles are in 52.0 grams of $ \text{NH}_3 $?

# Explanation:
## Step 1: Calculate the molar mass of $ \text{NH}_3 $
Molar mass of $ \text{N} = 14.01 \, \text{g/mol} $, $ \text{H} = 1.008 \, \text{g/mol} $:
$ \text{Molar Mass of } \text{NH}_3 = 14.01 + 3 \times 1.008 = 17.034 \, \text{g/mol} $

## Step 2: Convert grams to moles
$ \text{Moles of } \text{NH}_3 = \frac{52.0 \, \text{g}}{17.034 \, \text{g/mol}} \approx 3.053 \, \text{mol} $

## Step 3: Apply significant figures (3 sig figs, same as 52.0)
$ \text{Final Answer} \approx 3.05 \, \text{mol} $

# Answer:
$ \boxed{3.05 \, \text{mol}} $

### Question 3: How many grams of hydrogen are in $ 9.37 \times 10^{23} $ molecules of ammonium sulfate?

# Explanation:
## Step 1: Determine the formula for ammonium sulfate ($ (\text{NH}_4)_2\text{SO}_4 $)
Each $ (\text{NH}_4)_2\text{SO}_4 $ has $ 8 \, \text{H} $ atoms (2 $ \text{NH}_4^+ $ ions, each with 4 H).

## Step 2: Convert molecules to moles (using Avogadro’s number)
$ \text{Moles of } (\text{NH}_4)_2\text{SO}_4 = \frac{9.37 \times 10^{23} \, \text{molecules}}{6.022 \times 10^{23} \, \text{molecules/mol}} \approx 1.556 \, \text{mol} $

## Step 3: Moles of H atoms
Each $ (\text{NH}_4)_2\text{SO}_4 $ has 8 H atoms, so:
$ \text{Moles of H} = 1.556 \, \text{mol} \times 8 = 12.448 \, \text{mol} $

## Step 4: Convert moles of H to grams (molar mass of H = $ 1.008 \, \text{g/mol} $)
$ \text{Mass of H} = 12.448 \, \text{mol} \times 1.008 \, \text{g/mol} \approx 12.55 \, \text{g} $

## Step 5: Apply significant figures (3 sig figs, same as $ 9.37 \times 10^{23} $)
$ \text{Final Answer} \approx 12.6 \, \text{g} $

# Answer:
$ \boxed{12.6 \, \text{g}} $

### Question 4: How many moles of oxygen are in 4.88 moles of Iron (III) hydroxide?

# Explanation:
## Step 1: Determine the formula for Iron (III) hydroxide ($ \text{Fe(OH)}_3 $)
Each $ \text{Fe(OH)}_3 $ has 3 O atoms.

## Step 2: Moles of O atoms
$ \text{Moles of O} = \text{Moles of } \text{Fe(OH)}_3 \times 3 $
$ \text{Moles of O} = 4.88 \, \text{mol} \times 3 = 14.64 \, \text{mol} $

## Step 3: Apply significant figures (3 sig figs, same as 4.88)
$ \text{Final Answer} \approx 14.6 \, \text{mol} $

# Answer:
$ \boxed{14.6 \, \text{mol}} $

### Question 5: How many molecules are in 5.30 moles of calcium phosphate?

# Explanation:
## Step 1: Determine the formula for calcium phosphate ($ \text{Ca}_3(\text{PO}_4)_2 $)
Use Avogadro’s number to convert moles to molecules.

## Step 2: Convert moles to molecules
$ \text{Molecules} = \text{Moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} $
$ \text{Molecules} = 5.30 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 3.192 \times 10^{24} \, \text{molecules} $

## Step 3: Apply significant figures (3 sig figs, same as 5.30)
$ \text{Final Answer} \approx 3.19 \times 10^{24} \, \text{molecules} $

# Answer:
$ \boxed{3.19 \times 10^{24} \text{ molecules}} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1: How many molecules are there in 6.82 grams of \( \text{N}_2 \)?

Step 1: Calculate the molar mass of \( \text{N}_2 \)

Step 2: Convert grams to moles

Step 3: Convert moles to molecules (using Avogadro’s number \( 6.022 \times 10^{23} \, \text{molecules/mol} \))

Step 4: Apply significant figures (3 sig figs, same as 6.82)

Step 1: Calculate the molar mass of \( \text{NH}_3 \)

Step 2: Convert grams to moles

Step 3: Apply significant figures (3 sig figs, same as 52.0)

Step 1: Determine the formula for ammonium sulfate (\( (\text{NH}_4)_2\text{SO}_4 \))

Step 2: Convert molecules to moles (using Avogadro’s number)

Step 3: Moles of H atoms

Step 4: Convert moles of H to grams (molar mass of H = \( 1.008 \, \text{g/mol} \))

Step 5: Apply significant figures (3 sig figs, same as \( 9.37 \times 10^{23} \))

Answer:

Question 2: How many moles are in 52.0 grams of \( \text{NH}_3 \)?