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If a 375 -mL sample of neon gas is heated from 24 'C to 72 ' \(\mathrm{C}\) at constant pressure, what will be the volume of the sample at the higher temperature?

Short Answer

Expert verified
The final volume of the neon gas sample at 72 °C and constant pressure is approximately 436.5 mL. We calculate this by first converting the given temperatures from Celsius to Kelvin and then applying Charles's Law, (V1/T1)=(V2/T2), where V1 and T1 are the initial volume and temperature, respectively, and V2 and T2 are the final volume and temperature, respectively.

Step by step solution

01

Convert temperatures from Celsius to Kelvin

To convert temperatures from Celsius to Kelvin, we add 273.15 to the Celsius temperature. Initial temperature in Kelvin (T1): T1 = 24 °C + 273.15 = 297.15 K Final temperature in Kelvin (T2): T2 = 72 °C + 273.15 = 345.15 K
02

Apply Charles's Law and solve for final volume

Charles's Law states that the volume of a gas is directly proportional to its temperature, provided the pressure remains constant. Mathematically, it can be expressed as: (V1/T1)=(V2/T2) Where V1 and T1 are the initial volume and temperature, respectively, and V2 and T2 are the final volume and temperature, respectively. We are given the initial volume, V1 (375 mL), and we have calculated T1 and T2 using Step 1. Now we can solve for the final volume, V2: V2 = V1 * (T2 / T1) V2 = 375 mL * (345.15 K / 297.15 K) V2 ≈ 436.5 mL The final volume of the neon gas sample at 72 °C and constant pressure is approximately 436.5 mL.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gas Laws
Gas laws are fundamental principles that describe the behavior of gases in response to changes in pressure, volume, and temperature. One key aspect of these laws is their ability to predict the behavior of a gas under varying conditions, which is crucial in fields such as chemistry, physics, and engineering.

The cornerstone of gas law is the idea that gases tend to expand when heated and compress when cooled, all the while exerting pressure on their container. This expansion and compression can be quantified by specific gas laws, such as Boyle's Law (pressure-volume relationship), Charles's Law (temperature-volume relationship), and Gay-Lussac's Law (pressure-temperature relationship). When combined, these individual laws form the Combined Gas Law, which provides a comprehensive equation to account for simultaneous changes in pressure, volume, and temperature. Furthermore, when the number of molecules (or moles) of a gas is also factored in, the Ideal Gas Law emerges, encapsulating all of the separate gas laws into one overarching principle.
Temperature-Volume Relationship
The temperature-volume relationship of a gas is elegantly demonstrated by Charles's Law. This law states that the volume of a given amount of gas held at constant pressure is directly proportional to its Kelvin temperature. In other words, as the temperature of a gas increases, so does its volume, and vice versa.

When we talk about temperature in the context of gas laws, it's vital to use the Kelvin scale since it starts at absolute zero, the point at which particles theoretically have no kinetic energy and thus no motion. Utilizing temperatures in Kelvin allows us to apply Charles's Law correctly and avoid negative volumes, which don't make physical sense in this context. To better understand the concept in practice, a real-world example is helpful: Imagine a balloon exposed to heat, as the air inside the balloon warms up, its volume increases, causing the balloon to expand. This principle is utilized in technologies like hot air balloons and is an everyday demonstration of the temperature-volume relationship.
Kelvin Temperature Scale
The Kelvin temperature scale is an absolute temperature scale, meaning it begins at absolute zero, where all molecular motion stops. The scale is named after Lord Kelvin (William Thomson), who developed it in the mid-1800s. It's particularly important in the study of thermodynamics and gas laws because the Kelvin scale provides a direct measurement of the thermal energy within a substance.

The key distinction between the Kelvin scale and the Celsius or Fahrenheit scales is that the Kelvin scale does not have negative numbers. This characteristic simplifies the mathematical relationships in the gas laws, such as Charles's Law, making it the preferable scale for scientific calculations. To convert from Celsius to Kelvin, one simply adds 273.15 to the Celsius temperature, thus shifting the starting point from the freezing point of water to absolute zero. For example, the boiling point of water, 100 °C, is equivalent to 373.15 K in the Kelvin scale, and this consistent conversion is essential in ensuring accuracy when dealing with gas behavior at different temperatures.

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Most popular questions from this chapter

Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant. b. If the temperature of a gas increases from 25 ' \(\mathrm{C}\) to \(50 \mathrm{C},\) the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one-half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

Given each of the following sets of values for three of the gas variables, calculate the unknown quantity. a. \(P=21.2\) atm \(; V=142 \mathrm{~mL} ; n=0.432 \mathrm{~mol} ; T=? \mathrm{~K}\) b. \(P=?\) atm \(; V=1.23 \mathrm{~mL} ; n=0.000115 \mathrm{~mol} ; T=293 \mathrm{~K}\) c. \(P=755 \mathrm{~mm} \mathrm{Hg} ; V=? \mathrm{~mL} ; n=0.473 \mathrm{~mol} ; T=131 \mathrm{C}\)

Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc. $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose \(240 . \mathrm{mL}\) of hydrogen gas is collected at \(30 .^{\circ} \mathrm{C}\) and has a total pressure of 1.032 atm by this process. What is the partial pressure of hydrogen gas in the sample? How many moles of hydrogen gas are present in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor pressure of water is 32 torr at \(\left.30^{\circ} \mathrm{C} .\right)\)

If the pressure on a \(2.10 \times 10^{4} \mathrm{~mL}\) sample of gas is doubled at constant temperature, what will be the new volume of the gas?

Suppose a 24.3 -mL sample of helium gas at 25 and 1.01 atm is heated to \(50 .\) C and compressed to a volume of \(15.2 \mathrm{~mL}\). What will be the pressure of the sample?

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