Q: Step 3: Plug in the numbers and calculate.

$P = (4.283 \text{ moles} \times 0.08206 \text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}) \times 295.15 \text{ K}) / 50.0 \text{ L}$ $P = (103.737 \text{ L}\cdot\text{atm}) / 50.0 \text{ L}$ $P = 2.075 \text{ atm}$

Question 1

Step 2: Set up the rearranged equation.

Accepted Answer

We are solving for Pressure (P), so we use the rearranged formula: $P = (nRT) / V$.

Question 2

Step 3: Plug in the numbers and calculate.

Accepted Answer

$P = (4.283 	ext{ moles} 	imes 0.08206 	ext{ L}\cdot	ext{atm}/(	ext{mol}\cdot	ext{K}) 	imes 295.15 	ext{ K}) / 50.0 	ext{ L}$
$P = (103.737 	ext{ L}\cdot	ext{atm}) / 50.0 	ext{ L}$
$P = 2.075 	ext{ atm}$

Question 3

When to choose which?

Accepted Answer

If you are a student, a scuba diver, or a laboratory technician working at near-room temperatures and pressures under 10 atmospheres, the Ideal Gas Law is universally preferred. It is fast, requires no lookup tables for specific chemical parameters, and is accurate enough for 99% of daily tasks. If you are an engineer designing a cryogenic liquid nitrogen storage facility, or modeling the injection of pressurized methane into a deep-sea oil well at 400 atmospheres, the Ideal Gas Law is dangerously inadequate. In those high-stakes, extreme-environment scenarios, the computational burden of Peng-Robinson or Van der Waals is a mandatory cost of doing business safely.

Question 4

What happens if I use Fahrenheit or Celsius instead of Kelvin?

Accepted Answer

If you use Fahrenheit or Celsius, your calculation will be entirely incorrect, often resulting in negative pressures or volumes, which are physically impossible. The Ideal Gas Law relies on proportional multiplication and division. Because 0°C and 0°F do not represent zero kinetic energy, scaling these temperatures mathematically breaks the proportions. Kelvin is an absolute scale where 0 K means zero molecular motion, making it the only mathematically valid temperature scale for thermodynamic equations.

Question 5

Why are there so many different values for the Gas Constant (R)?

Accepted Answer

The physical constant 'R' represents the exact same amount of fundamental thermodynamic energy in every version, but it is expressed in different "languages" (units). Just as 1 inch and 2.54 centimeters represent the exact same physical distance, $0.08206 	ext{ L}\cdot	ext{atm}/(	ext{mol}\cdot	ext{K})$ and $8.314 	ext{ J}/(	ext{mol}\cdot	ext{K})$ represent the exact same proportionality. You choose the R value that contains the specific units of pressure and volume you are currently working with, allowing those units to cancel out properly during the algebra.

Question 6

Can I use the Ideal Gas Law for liquids or solids?

Accepted Answer

Absolutely not. The Ideal Gas Law is explicitly an equation of state for gases. Liquids and solids are relatively incompressible because their molecules are already in direct physical contact with one another. Their volumes do not change significantly with pressure, and their behavior is governed by entirely different, much more complex physical laws regarding fluid dynamics and crystalline structures. Applying PV=nRT to liquid water will yield wildly incorrect and useless results.

Question 7

Does the Ideal Gas Law work for gas mixtures, like air?

Accepted Answer

Yes, it works exceptionally well for gas mixtures, thanks to Dalton's Law of Partial Pressures. Because the Ideal Gas Law assumes gas molecules do not interact with one another, the identity of the gas does not matter. If you have a container with 1 mole of oxygen and 3 moles of nitrogen, you simply treat it as 4 total moles of "gas." You plug $n = 4$ into the equation, and the resulting pressure calculation will perfectly represent the total combined pressure of the atmospheric mixture.

Question 8

How do I handle a problem where the gas is collected "over water"?

Accepted Answer

When a gas is collected over liquid water in a laboratory experiment, the trapped gas is not pure; it is a mixture of the target gas and evaporated water vapor. To use the Ideal Gas Law to find the amount of your target gas, you must first subtract the "vapor pressure of water" (which depends on the room's temperature and can be found in reference tables) from the total measured pressure of the container. Once you subtract the water's pressure, you plug the remaining pressure into PV=nRT to solve for the moles of your specific dry gas.

Question 9

What is the difference between an Ideal Gas and a Real Gas?

Accepted Answer

An ideal gas is a mathematical fiction where molecules are treated as infinitely small dots that never attract or repel each other. A real gas consists of actual physical atoms that take up microscopic amounts of space and exert weak electromagnetic pulls on one another. Under normal, everyday conditions, real gases behave so similarly to the mathematical fiction that the difference is negligible. However, under extreme cold or extreme pressure, real gases deviate from the math, requiring more complex formulas like the Van der Waals equation to model accurately.

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