Answer :
The temperature of the carbon dioxide sample will be -26.1°C after it changes to 1440 mm Hg and 4200 mL by using the combined gas law equation: (P1 * V1) / T1 = (P2 * V2) / T2.
When the pressure and volume of a gas change, we can use the combined gas law to calculate the new temperature. The combined gas law states that the ratio of the initial pressure to the initial temperature is equal to the ratio of the final pressure to the final temperature, assuming the amount of gas and the volume are constant.
In this case, the initial pressure is 1540 mm Hg, the initial temperature is -33.5°C, the final pressure is 1440 mm Hg, and the final volume is 4200 mL. We need to find the final temperature.
Using the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Substituting the given values:
(1540 mm Hg * 3700 mL) / (-33.5°C) = (1440 mm Hg * 4200 mL) / T2
We can cross-multiply and solve for T2:
(1540 mm Hg * 3700 mL) * T2 = (1440 mm Hg * 4200 mL) * (-33.5°C)
T2 = ((1440 mm Hg * 4200 mL) * (-33.5°C)) / (1540 mm Hg * 3700 mL)
Calculating the value, T2 comes out to be -26.1°C.
Therefore, the temperature of the carbon dioxide sample will be -26.1°C after it changes to 1440 mm Hg and 4200 mL.
The given problem involves the change in pressure, volume, and temperature of a carbon dioxide sample. To determine the final temperature, we can apply the combined gas law, which relates the initial and final conditions of a gas when the amount and volume remain constant.
Using the combined gas law equation, we can establish a proportionality between the initial pressure, volume, and temperature, and the final pressure, volume, and temperature. By rearranging the equation and substituting the given values, we isolate the final temperature, which we need to calculate.
Upon solving the equation, we find that the final temperature (T2) is equal to -26.1°C. This indicates that the carbon dioxide sample, initially at -33.5°C, experiences a decrease in temperature as it changes to the new conditions of 1440 mm Hg and 4200 mL.
The negative sign signifies that the sample's temperature decreases, implying a cooling effect. The magnitude of this decrease is approximately 7.6°C. Therefore, the final temperature is -26.1°C.
Understanding gas laws and their applications allows us to predict the behavior of gases under varying conditions. The combined gas law, which combines Boyle's, Charles's, and Gay-Lussac's laws, enables us to analyze the relationship between pressure, volume, and temperature. This knowledge finds utility in various fields, such as chemistry, physics, and engineering, helping us comprehend the behavior of gases in different scenarios.
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