At constant pressure, at what temperature will the volume of a gas become twice its volume at 0 °C?

Q: At constant pressure, at what temperature will the volume of a gas become twice its volume at 0 °C?

546 K - Charles’ Law describes the relationship between the volume of a gas and its absolute temperature when the pressure is kept constant. The law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature measured in Kelvin. Mathematically, it is expressed as: V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}T1V1=T2V2 where V1V_1V1 and V2V_2V2 are the initial and final volumes, and T1T_1T1 and T2T_2T2 are the corresponding absolute temperatures. In this problem, the initial temperature of the gas is 0 °C, which is equal to 273 K. The question asks for the temperature at which the gas volume becomes exactly twice the initial volume. Substituting into Charles’ Law, we set V2=2V1V_2 = 2V_1V2=2V1. This leads to: V1273=2V1T2\frac{V_1}{273} = \frac{2V_1}{T_2}273V1=T22V1 Solving gives T2=546KT_2 = 546 KT2=546K. It is important to note that temperatures in gas law calculations must always be expressed in Kelvin, not in Celsius. Kelvin is the absolute temperature scale where 0 K represents absolute zero, the lowest possible temperature. If we incorrectly used Celsius in this problem, the result would not be valid. At 546 K, which corresponds to 273 °C, the gas volume becomes twice its original volume at 0 °C under constant pressure. This is a direct consequence of the proportionality between volume and temperature. The doubling of volume shows the predictive power of gas laws in explaining the behavior of gases under changing conditions. Charles’ Law is fundamental in understanding real-life processes such as hot air balloons, where heating the air increases its volume, causing the balloon to rise. It also explains why gases expand when heated. Such relationships between gas properties are studied in physical chemistry to understand both ideal and real gas behaviors.

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Accepted Answer

546 K - Charles&rsquo; Law describes the relationship between the volume of a gas and its absolute temperature when the pressure is kept constant. The law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature measured in Kelvin. Mathematically, it is expressed as:
V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}T1V1=T2V2
where V1V_1V1 and V2V_2V2 are the initial and final volumes, and T1T_1T1 and T2T_2T2 are the corresponding absolute temperatures.
In this problem, the initial temperature of the gas is 0 &deg;C, which is equal to 273 K. The question asks for the temperature at which the gas volume becomes exactly twice the initial volume. Substituting into Charles&rsquo; Law, we set V2=2V1V_2 = 2V_1V2=2V1. This leads to:
V1273=2V1T2\frac{V_1}{273} = \frac{2V_1}{T_2}273V1=T22V1
Solving gives T2=546KT_2 = 546 KT2=546K.
It is important to note that temperatures in gas law calculations must always be expressed in Kelvin, not in Celsius. Kelvin is the absolute temperature scale where 0 K represents absolute zero, the lowest possible temperature. If we incorrectly used Celsius in this problem, the result would not be valid.
At 546 K, which corresponds to 273 &deg;C, the gas volume becomes twice its original volume at 0 &deg;C under constant pressure. This is a direct consequence of the proportionality between volume and temperature. The doubling of volume shows the predictive power of gas laws in explaining the behavior of gases under changing conditions.
Charles&rsquo; Law is fundamental in understanding real-life processes such as hot air balloons, where heating the air increases its volume, causing the balloon to rise. It also explains why gases expand when heated. Such relationships between gas properties are studied in physical chemistry to understand both ideal and real gas behaviors.

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