Gay-Lussac's Law

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Questions and Answers

What is the standard unit of measure for temperature used in gas law calculations, and why is it preferred?

Kelvin (K). It is preferred because it starts at absolute zero, avoiding negative values that would complicate calculations.

Explain in your own words the relationship between pressure and temperature of a gas as described by Gay-Lussac's Law.

Gay-Lussac's Law states that the pressure of a gas is directly proportional to its temperature when the volume and amount of gas are held constant. If you increase the temperature, the pressure increases proportionally, and vice versa.

Convert 25 degrees Celsius to Kelvin. Show your work.

$T_K = T_C + 273.15 = 25 + 273.15 = 298.15 K$

A gas is at a pressure of 3 atm and a temperature of 300 K. If the temperature is increased to 450 K, what is the new pressure, assuming the volume and number of moles are constant?

$rac{P_1}{T_1} = rac{P_2}{T_2} \Rightarrow P_2 = rac{P_1T_2}{T_1} = rac{3 ext{ atm} \cdot 450 ext{ K}}{300 ext{ K}} = 4.5 ext{ atm}$ Signup and view all the answers

What condition must be met for Gay-Lussac's Law to be applicable when analyzing a gas?

The volume and the amount of gas (number of moles) must be held constant. Signup and view all the answers

A container of gas has a pressure of 2 atm at 27 degrees Celsius. If the pressure is increased to 4 atm, what is the new temperature in Celsius?

$T_1 = 27 + 273.15 = 300.15 ext{ K}$. $rac{P_1}{T_1} = rac{P_2}{T_2} \Rightarrow T_2 = rac{P_2T_1}{P_1} = rac{4 ext{ atm} \cdot 300.15 ext{ K}}{2 ext{ atm}} = 600.3 ext{ K}$. $T_2 = 600.3 - 273.15 = 327.15 ext{C}$ Signup and view all the answers

Explain how the relationship described in Gay-Lussac's Law is observed in everyday scenarios.

The increasing pressure in a car tire on a hot day is a practical example. As the temperature rises, so does the pressure inside the tire. Signup and view all the answers

Convert 750 mmHg to atm.

$rac{750 ext{ mmHg}}{760 ext{ mmHg/atm}} = 0.987 ext{ atm}$ Signup and view all the answers

A rigid container holds a gas at a pressure of 1.5 atm at 20 degrees Celsius. If the container is heated to 60 degrees Celsius, what will be the final pressure inside the container?

$T_1 = 20 + 273.15 = 293.15 ext{ K}$. $T_2 = 60 + 273.15 = 333.15 ext{ K}$. $rac{P_1}{T_1} = rac{P_2}{T_2} \Rightarrow P_2 = rac{P_1T_2}{T_1} = rac{1.5 ext{ atm} \cdot 333.15 ext{ K}}{293.15 ext{ K}} = 1.71 ext{ atm}$ Signup and view all the answers

Why is it important to use absolute temperature (Kelvin) in Gay-Lussac's Law instead of Celsius or Fahrenheit?

Kelvin is an absolute scale starting from absolute zero which means that there is a direct proportional relationship between temperature and pressure. Celsius and Fahrenheit are relative scales and include negative values. Signup and view all the answers

A gas in a sealed container has a pressure of 120 kPa at a temperature of 20C. If the temperature is raised to 50C, what will the new pressure be in kPa?

First convert Celsius to Kelvin: $T_1 = 20 + 273.15 = 293.15K$ and $T_2 = 50 + 273.15 = 323.15K$. Then use Gay-Lussac's Law: $P_2 = P_1 * (T_2 / T_1) = 120 ext{ kPa} * (323.15 ext{ K} / 293.15 ext{ K}) = 132.36 ext{ kPa}$ Signup and view all the answers

If a gas exerts a pressure of 800 torr at 300 K, what pressure will it exert at 400 K, assuming constant volume and amount of gas?

Using Gay-Lussac's Law: $P_2 = P_1 * (T_2 / T_1) = 800 ext{ torr} * (400 ext{ K} / 300 ext{ K}) = 1066.67 ext{ torr}$ Signup and view all the answers

A balloon contains air at 27C and a pressure of 1 atm. If the temperature is increased to 227C, what is the new pressure inside the balloon? Assume the volume remains constant.

Convert Celsius to Kelvin: $T_1 = 27 + 273.15 = 300.15K$ and $T_2 = 227 + 273.15 = 500.15K$. Use Gay-Lussac's Law: $P_2 = P_1 * (T_2 / T_1) = 1 ext{ atm} * (500.15 ext{ K} / 300.15 ext{ K}) = 1.67 ext{ atm}$ Signup and view all the answers

A gas has a pressure of 1.2 atm at 25C. What is the pressure if the temperature is decreased to -25C?

Convert Celsius to Kelvin: $T_1 = 25 + 273.15 = 298.15 K$ and $T_2 = -25 + 273.15 = 248.15 K$. Use Gay-Lussac's Law: $P_2 = P_1 * (T_2 / T_1) = 1.2 ext{ atm} * (248.15 ext{ K} / 298.15 ext{ K}) = 0.998 ext{ atm}$ Signup and view all the answers

If a gas is heated from 30C to 60C and its initial pressure is 150 kPa, what is its final pressure, assuming the volume is constant?

Convert Celsius to Kelvin: $T_1 = 30 + 273.15 = 303.15 K$ and $T_2 = 60 + 273.15 = 333.15 K$. Use Gay-Lussac's Law: $P_2 = P_1 * (T_2 / T_1) = 150 ext{ kPa} * (333.15 ext{ K} / 303.15 ext{ K}) = 165.02 ext{ kPa}$ Signup and view all the answers

Flashcards

What is temperature?

A measure of hotness or coldness expressed in defined units.

How do you convert Fahrenheit to Celsius?

°C = (°F - 32) × 5/9