The Ideal Gas Law - AP Physics 2
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What happens to pressure when volume decreases at constant $n$ and $T$?
What happens to pressure when volume decreases at constant $n$ and $T$?
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Pressure increases. Gas molecules compress into smaller space, creating higher pressure.
Pressure increases. Gas molecules compress into smaller space, creating higher pressure.
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Identify the relationship between moles and volume in the Ideal Gas Law.
Identify the relationship between moles and volume in the Ideal Gas Law.
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Directly proportional. More gas molecules occupy more space (Avogadro's Law).
Directly proportional. More gas molecules occupy more space (Avogadro's Law).
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What does the variable $T$ represent in the Ideal Gas Law?
What does the variable $T$ represent in the Ideal Gas Law?
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Temperature in Kelvin. Absolute temperature scale starting at absolute zero.
Temperature in Kelvin. Absolute temperature scale starting at absolute zero.
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Determine $V$ for $P = 1.5$ atm, $n = 2$ mol, $T = 298$ K.
Determine $V$ for $P = 1.5$ atm, $n = 2$ mol, $T = 298$ K.
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$V = 32.6$ L. Using $PV = nRT$: $V = \frac{(2)(0.0821)(298)}{1.5} = 32.6$ L.
$V = 32.6$ L. Using $PV = nRT$: $V = \frac{(2)(0.0821)(298)}{1.5} = 32.6$ L.
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What does the variable $R$ represent in the Ideal Gas Law?
What does the variable $R$ represent in the Ideal Gas Law?
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Ideal gas constant. Universal proportionality constant relating gas properties.
Ideal gas constant. Universal proportionality constant relating gas properties.
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Calculate the volume if $P = 2$ atm, $n = 1$ mol, $T = 273$ K.
Calculate the volume if $P = 2$ atm, $n = 1$ mol, $T = 273$ K.
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$V = 11.2$ L. Using $PV = nRT$: $V = \frac{(1)(0.0821)(273)}{2} = 11.2$ L.
$V = 11.2$ L. Using $PV = nRT$: $V = \frac{(1)(0.0821)(273)}{2} = 11.2$ L.
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What happens to pressure when volume decreases at constant $n$ and $T$?
What happens to pressure when volume decreases at constant $n$ and $T$?
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Pressure increases. Gas molecules compress into smaller space, creating higher pressure.
Pressure increases. Gas molecules compress into smaller space, creating higher pressure.
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Identify the relationship between volume and temperature in the Ideal Gas Law.
Identify the relationship between volume and temperature in the Ideal Gas Law.
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Directly proportional. Both increase or decrease together (Charles's Law).
Directly proportional. Both increase or decrease together (Charles's Law).
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Find the number of moles for $P = 4$ atm, $V = 15$ L, $T = 300$ K.
Find the number of moles for $P = 4$ atm, $V = 15$ L, $T = 300$ K.
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$n = 2.44$ mol. Using $PV = nRT$: $n = \frac{(4)(15)}{(0.0821)(300)} = 2.44$ mol.
$n = 2.44$ mol. Using $PV = nRT$: $n = \frac{(4)(15)}{(0.0821)(300)} = 2.44$ mol.
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What units must pressure be in for the Ideal Gas Law when using $R = 0.0821$?
What units must pressure be in for the Ideal Gas Law when using $R = 0.0821$?
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Atmospheres (atm). Required unit to match the gas constant $R$ value.
Atmospheres (atm). Required unit to match the gas constant $R$ value.
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What happens to pressure when temperature decreases at constant $V$ and $n$?
What happens to pressure when temperature decreases at constant $V$ and $n$?
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Pressure decreases. Lower kinetic energy reduces molecular collisions with walls.
Pressure decreases. Lower kinetic energy reduces molecular collisions with walls.
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Find the volume of 1 mole of gas at 1 atm and 273 K.
Find the volume of 1 mole of gas at 1 atm and 273 K.
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$V = 22.4$ L. Standard molar volume at STP conditions.
$V = 22.4$ L. Standard molar volume at STP conditions.
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Calculate pressure when 0.5 mol of gas is at 350 K in a 5 L container.
Calculate pressure when 0.5 mol of gas is at 350 K in a 5 L container.
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$P = 2.87$ atm. Using $PV = nRT$: $P = \frac{(0.5)(0.0821)(350)}{5} = 2.87$ atm.
$P = 2.87$ atm. Using $PV = nRT$: $P = \frac{(0.5)(0.0821)(350)}{5} = 2.87$ atm.
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Calculate the pressure if $n = 1$ mol, $V = 22.4$ L, $T = 273$ K.
Calculate the pressure if $n = 1$ mol, $V = 22.4$ L, $T = 273$ K.
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$P = 1$ atm. Using $PV = nRT$: $P = \frac{(1)(0.0821)(273)}{22.4} = 1$ atm.
$P = 1$ atm. Using $PV = nRT$: $P = \frac{(1)(0.0821)(273)}{22.4} = 1$ atm.
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Convert 100°C to Kelvin for use in gas law calculations.
Convert 100°C to Kelvin for use in gas law calculations.
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$373.15$ K. Add 273.15 to Celsius temperature.
$373.15$ K. Add 273.15 to Celsius temperature.
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Find the temperature if $P = 3$ atm, $V = 10$ L, $n = 1$ mol.
Find the temperature if $P = 3$ atm, $V = 10$ L, $n = 1$ mol.
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$T = 366$ K. Using $PV = nRT$: $T = \frac{(3)(10)}{(1)(0.0821)} = 366$ K.
$T = 366$ K. Using $PV = nRT$: $T = \frac{(3)(10)}{(1)(0.0821)} = 366$ K.
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Identify the units for $R$ when pressure is in Pascals.
Identify the units for $R$ when pressure is in Pascals.
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Joules per mole Kelvin. Energy units appropriate for Pascal pressure measurements.
Joules per mole Kelvin. Energy units appropriate for Pascal pressure measurements.
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In the Ideal Gas Law, what units must volume be in when using $R = 0.0821$?
In the Ideal Gas Law, what units must volume be in when using $R = 0.0821$?
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Liters (L). Volume unit that corresponds to the standard $R$ value.
Liters (L). Volume unit that corresponds to the standard $R$ value.
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Determine $V$ for $P = 1.5$ atm, $n = 2$ mol, $T = 298$ K.
Determine $V$ for $P = 1.5$ atm, $n = 2$ mol, $T = 298$ K.
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$V = 32.6$ L. Using $PV = nRT$: $V = \frac{(2)(0.0821)(298)}{1.5} = 32.6$ L.
$V = 32.6$ L. Using $PV = nRT$: $V = \frac{(2)(0.0821)(298)}{1.5} = 32.6$ L.
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Find the pressure of 2 moles of gas at 300 K in a 10 L container.
Find the pressure of 2 moles of gas at 300 K in a 10 L container.
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$P = 4.92$ atm. Using $PV = nRT$: $P = \frac{(2)(0.0821)(300)}{10} = 4.92$ atm.
$P = 4.92$ atm. Using $PV = nRT$: $P = \frac{(2)(0.0821)(300)}{10} = 4.92$ atm.
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What is the temperature if $P = 5$ atm, $V = 20$ L, $n = 2$ mol?
What is the temperature if $P = 5$ atm, $V = 20$ L, $n = 2$ mol?
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$T = 609$ K. Using $PV = nRT$: $T = \frac{(5)(20)}{(2)(0.0821)} = 609$ K.
$T = 609$ K. Using $PV = nRT$: $T = \frac{(5)(20)}{(2)(0.0821)} = 609$ K.
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What happens to volume when temperature increases at constant $P$ and $n$?
What happens to volume when temperature increases at constant $P$ and $n$?
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Volume increases. Higher kinetic energy causes gas to expand.
Volume increases. Higher kinetic energy causes gas to expand.
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If $T$ doubles and $n$ and $V$ are constant, what happens to $P$?
If $T$ doubles and $n$ and $V$ are constant, what happens to $P$?
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Pressure doubles. Temperature is directly proportional to pressure.
Pressure doubles. Temperature is directly proportional to pressure.
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What is the ideal gas constant $R$ value in $J/(mol \times K)$?
What is the ideal gas constant $R$ value in $J/(mol \times K)$?
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$8.314 \text{ J}/(\text{mol} \times \text{K})$. Used when pressure is in Pascals and volume in cubic meters.
$8.314 \text{ J}/(\text{mol} \times \text{K})$. Used when pressure is in Pascals and volume in cubic meters.
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Identify the units for $R$ when using $8.314$ as the constant.
Identify the units for $R$ when using $8.314$ as the constant.
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$J/(mol \times K)$. Energy per amount per temperature unit.
$J/(mol \times K)$. Energy per amount per temperature unit.
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If $V$ is halved and $n$ and $T$ are constant, what happens to $P$?
If $V$ is halved and $n$ and $T$ are constant, what happens to $P$?
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Pressure doubles. Volume is inversely proportional to pressure.
Pressure doubles. Volume is inversely proportional to pressure.
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Determine $n$ for $P = 2$ atm, $V = 5$ L, $T = 298$ K.
Determine $n$ for $P = 2$ atm, $V = 5$ L, $T = 298$ K.
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$n = 0.41$ mol. Using $PV = nRT$: $n = \frac{(2)(5)}{(0.0821)(298)} = 0.41$ mol.
$n = 0.41$ mol. Using $PV = nRT$: $n = \frac{(2)(5)}{(0.0821)(298)} = 0.41$ mol.
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What does the variable $T$ represent in the Ideal Gas Law?
What does the variable $T$ represent in the Ideal Gas Law?
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Temperature in Kelvin. Absolute temperature scale starting at absolute zero.
Temperature in Kelvin. Absolute temperature scale starting at absolute zero.
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Identify the relationship between moles and volume in the Ideal Gas Law.
Identify the relationship between moles and volume in the Ideal Gas Law.
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Directly proportional. More gas molecules occupy more space (Avogadro's Law).
Directly proportional. More gas molecules occupy more space (Avogadro's Law).
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Identify the relationship between pressure and volume in the Ideal Gas Law.
Identify the relationship between pressure and volume in the Ideal Gas Law.
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Inversely proportional. When one increases, the other decreases (Boyle's Law).
Inversely proportional. When one increases, the other decreases (Boyle's Law).
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