Answer :
Answer:
The initial number of moles is approximately 1.083 moles.
Explanation:
To solve this problem, we can use the ideal gas law equation, which states:
[tex]\[ PV = nRT \][/tex]
Where:
- ( P ) is the pressure (constant in this case),
- ( V ) is the volume,
- ( n ) is the number of moles,
- ( R ) is the ideal gas constant,
- ( T )is the temperature (constant in this case).
Since pressure and temperature are constant, we can simplify the equation to:
[tex]\[ V_1 \cdot n_1 = V_2 \cdot n_2 \][/tex]
Where:
-
[tex]( V_1 ) and ( V_2 )[/tex]
are the initial and final volumes, respectively,
-
[tex]( n_1 )[/tex]
and
[tex]( n_2 )[/tex]
are the initial and final number of moles, respectively.
Given:
-
[tex]( V_1 = 3.62 , \text{L} )[/tex]
-
[tex]( V_2 = 3.86 , \text{L} )[/tex]
-
[tex]( n_2 = 1.02 , \text{moles} )[/tex]
Let's solve for
[tex]( n_1 ):[/tex]
[tex]\[ V_1 \cdot n_1 = V_2 \cdot n_2 \][/tex]
[tex]\[ 3.62 \cdot n_1 = 3.86 \cdot 1.02 \][/tex]
Now, solve for
[tex]( n_1 ):[/tex]
[tex]\[ n_1 = \frac{3.86 \cdot 1.02}{3.62} \][/tex]
[tex]\[ n_1 \approx 1.083 \][/tex]
Therefore, the initial number of moles is approximately
[tex]1.083 \: moles[/tex]
