How many moles of gas are contained in a sample of gas that occupies 26.6 L at 0.8 atm and 345.1 K?
The correct answer and explanation is:
To calculate the number of moles of gas, we use the Ideal Gas Law: PV=nRTPV = nRT
Where:
- PP = pressure in atm = 0.8 atm
- VV = volume in liters = 26.6 L
- nn = number of moles = ?
- RR = ideal gas constant = 0.0821 L·atm/mol·K
- TT = temperature in Kelvin = 345.1 K
Step 1: Rearranging the Ideal Gas Law
n=PVRTn = \frac{PV}{RT}
Step 2: Plug in the values
n=(0.8 atm)×(26.6 L)(0.0821 L\cdotpatm/mol\cdotpK)×(345.1 K)n = \frac{(0.8\ \text{atm}) \times (26.6\ \text{L})}{(0.0821\ \text{L·atm/mol·K}) \times (345.1\ \text{K})} n=21.2828.33171≈0.751molesn = \frac{21.28}{28.33171} \approx 0.751 moles
✅ Final Answer:
0.751 moles\boxed{0.751\ \text{moles}}
🔬 Explanation (Approx. 300 words):
The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It assumes ideal behavior of gas particles, meaning they have negligible volume and no intermolecular forces. This law is generally accurate for many gases under normal conditions.
In this question, we’re given:
- Volume (V) = 26.6 liters,
- Pressure (P) = 0.8 atmospheres,
- Temperature (T) = 345.1 K.
We use the ideal gas constant (R) as 0.0821 when pressure is in atm and volume is in liters. Rearranging the formula allows us to isolate and solve for nn, the number of moles.
When we substitute the values into the formula, the units cancel out appropriately, leaving us with moles as the unit, which is what we want.
The calculated value, approximately 0.751 moles, represents the amount of gas particles (in terms of Avogadro’s number) present in the sample under the specified conditions.
This type of problem is common in chemistry and helps scientists determine how much gas is available in reactions, how gases behave under different conditions, and how to scale experiments accurately.