Answer :
Answer:
To determine the final temperature needed to cause the volume of the gas to change from 4.00 L to 50 L, we can use Charles's Law. Charles's Law states that for a given amount of gas at constant pressure, the volume of the gas is directly proportional to its temperature in Kelvin. The law can be expressed as:
1
1
=
2
2
T
1
V
1
=
T
2
V
2
where
1
V
1
and
2
V
2
are the initial and final volumes, respectively, and
1
T
1
and
2
T
2
are the initial and final temperatures, respectively.
Given:
Initial volume,
1
=
4.00
V
1
=4.00 L
Final volume,
2
=
50
V
2
=50 L
Initial temperature,
1
=
0
∘
C
T
1
=0
∘
C
First, we need to convert the initial temperature from degrees Celsius to Kelvin. The Kelvin temperature scale can be obtained by adding 273.15 to the Celsius temperature:
1
=
0
∘
C
+
273.15
=
273.15
K
T
1
=0
∘
C+273.15=273.15 K
Now, using Charles's Law, we can solve for the final temperature
2
T
2
:
1
1
=
2
2
T
1
V
1
=
T
2
V
2
Rearranging to solve for
2
T
2
:
2
=
1
×
2
1
T
2
=T
1
×
V
1
V
2
Substituting the known values:
2
=
273.15
K
×
50
L
4.00
L
T
2
=273.15 K×
4.00 L
50 L
2
=
273.15
K
×
12.5
T
2
=273.15 K×12.5
2
=
3414.375
K
T
2
=3414.375 K
Finally, convert the temperature back to degrees Celsius by subtracting 273.15 from the Kelvin temperature:
2
=
3414.375
K
−
273.15
=
3141.22
5
∘
C
T
2
=3414.375 K−273.15=3141.225
∘
C
Thus, the final temperature needed to cause the volume of the gas to change to 50 L is approximately
3141.22
5
∘
C
3141.225
∘
C.
Explanation:
