To determine the mass, in grams, of 2.88 moles of glycine [tex]\( (C_2H_5NO_2) \)[/tex], we need to follow these detailed steps:
### Step 1: Calculate the molar mass of glycine
First, we determine the molar mass of glycine by summing the molar masses of its constituent elements based on its molecular formula [tex]\( C_2H_5NO_2 \)[/tex].
- Carbon (C): There are 2 carbon atoms.
[tex]\[
2 \times 12.01 \text{ g/mol} = 24.02 \text{ g/mol}
\][/tex]
- Hydrogen (H): There are 5 hydrogen atoms.
[tex]\[
5 \times 1.008 \text{ g/mol} = 5.04 \text{ g/mol}
\][/tex]
- Nitrogen (N): There is 1 nitrogen atom.
[tex]\[
1 \times 14.01 \text{ g/mol} = 14.01 \text{ g/mol}
\][/tex]
- Oxygen (O): There are 2 oxygen atoms.
[tex]\[
2 \times 16.00 \text{ g/mol} = 32.00 \text{ g/mol}
\][/tex]
Now, we sum these values:
[tex]\[
24.02 \text{ g/mol} + 5.04 \text{ g/mol} + 14.01 \text{ g/mol} + 32.00 \text{ g/mol} = 75.07 \text{ g/mol}
\][/tex]
Thus, the molar mass of glycine is [tex]\( 75.07 \text{ g/mol} \)[/tex].
### Step 2: Calculate the mass of glycine for 2.88 moles
To find the mass of glycine, we use the formula:
[tex]\[
\text{Mass} = \text{Moles} \times \text{Molar Mass}
\][/tex]
Given [tex]\( 2.88 \)[/tex] moles of glycine:
[tex]\[
\text{Mass} = 2.88 \text{ moles} \times 75.07 \text{ g/mol}
\][/tex]
Multiplying these values:
[tex]\[
\text{Mass} = 216.2016 \text{ grams}
\][/tex]
### Step 3: Round the result to three significant figures
To express the mass correctly, we round the value to three significant figures.
So, [tex]\( 216.2016 \)[/tex] grams rounded to three significant figures is:
[tex]\[
216.202 \text{ grams}
\][/tex]
### Final Answer
The mass of 2.88 moles of glycine [tex]\( (C_2H_5NO_2) \)[/tex] is [tex]\( 216.202 \)[/tex] grams.
