Answer: The final pressure inside the tank will be B. 18.05 atm. Gay-Lussac's law is used to predict the changes in pressure or temperature of gases. According to this law, there is a direct relationship between pressure and temperature. As the temperature of gas increases, so, too, will the pressure increase and vice versa.
Further Explanation:
We use the mathematical expression of Gay-Lussac's law to find the final pressure in the tank:
[tex]\frac{P_{initial}}{T_{initial}} \ = \frac{P_{final}}{T_{final}}[/tex]
It is very important to note that when using this equation, all temperatures must be expressed in Kelvin. The conversion from degree Celsius to Kelvin is:
[tex]T \ (in \ K) \ = T \ (in \ deg.\ C) \ +\ 273.15[/tex]
In the problem, we are given the following information:
P(initial) = 23 atm
T(initial) = 293 K
P(final) = ?
T(final) = 230 K
Plugging in these values in the Gay-Lussac Equation, we get:
[tex]\frac{23\ atm}{293 \ K} \ = \ \frac{P_{final}}{230\ K} \\P_{final} \ = \frac{(23 \ atm) \ (230 \ K)}{293 \ K}\\P_{final} \ = \ 18.05 \ atm[/tex]
The tank was moved from a hotter to a cooler place. At cooler temperatures, gas particles move slower and frequency and strength of their collisions with each other and the wall of the containers decrease. This leads to a decrease in the pressure. Thus, the pressure drops from 23 atm to 18.05 atm when the tank is inside the freezer.
Learn More:
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Keyword: Gas Pressure, Temperature, Gay-Lussac's Law
