Answer:
The pressure in the bottle is 826 mmHg
Explanation:
In this case it is assumed that the volume of the soda bottle does not change, so it remains constant with a value of 2.00 L. Then it is possible to apply the Gay Lussac law.
This law indicates that when there is a constant volume, as the temperature increases, the gas pressure increases. And when the temperature decreases, gas pressure decreases. That is, the gas pressure is directly proportional to its temperature.
Gay-Lussac's law can be expressed mathematically as follows:
[tex]\frac{P}{T}=k[/tex]
Where P = pressure, T = temperature and K = Constant
Having a gas that is at a pressure P1 and a temperature T1, as the temperature varies to a new T2 value, then the pressure will change to P2. It is then fulfilled:
[tex]\frac{P1}{T1} =\frac{P2}{T2}[/tex]
Remember that the temperature must be in degrees Kelvin (° K) and that 0 ° C is 273.15 ° K
In this case you know:
Replacing:
[tex]\frac{728 mmHg}{298.15K} =\frac{P2}{338.15K}[/tex]
Resolving you get:
[tex]\frac{728 mmHg}{298.15K} *338.15K=P2[/tex]
P2=825.67 mmHg≅826 mmHg
The pressure in the bottle is 826 mmHg
The pressure of the bottle is 825.7 mmHg
The parameters given in the question are
Pressure 1= 728 mmHg
Temperature 1= 25°C
= 25+273
T1= 298K
Temperature 2= 65°C
= 65 +273
= 338K
P1/T1= P2/T2
728/298= P2/338
Cross multiply
298 × P2= 728 × 338
298 × P2= 246,064
P2= 246,064/298
P2= 825.7
Hence the pressure in the bottle is 825.7 mmHg
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