Question
where you live?(11.8) KN A 41. 4.000times 10^3 L of propane gas is held in a tank at 25^circ C The tank has a moveable diaphragm to keep the pressure constant at 200 kPa. If the temperature falls to -5^circ C on a cold winter day,what volume will the gas occupy? (11.8)T/I
Solution
4.4
(263 Votes)
Sasha
Master · Tutor for 5 years
Answer
Here's how to solve this problem using the combined gas law:**Understanding the Combined Gas Law**The combined gas law relates the pressure, volume, and temperature of a gas under two different sets of conditions, assuming the amount of gas (number of moles) remains constant. The formula is:(P₁V₁)/T₁ = (P₂V₂)/T₂Where:* P₁ and P₂ are the initial and final pressures.* V₁ and V₂ are the initial and final volumes.* T₁ and T₂ are the initial and final temperatures (in Kelvin).**Important Note:** Temperatures *must* be converted to Kelvin for this equation to work correctly.**1. Convert Temperatures to Kelvin:*** T₁ = 25°C + 273.15 = 298.15 K* T₂ = -5°C + 273.15 = 268.15 K**2. Identify Known Values:*** P₁ = 200 kPa* V₁ = 4.000 x 10³ L* T₁ = 298.15 K* P₂ = 200 kPa (pressure is constant)* T₂ = 268.15 K**3. Solve for V₂:**We want to find V₂, the final volume. Rearrange the combined gas law equation to solve for V₂:V₂ = (P₁V₁T₂)/(T₁P₂)**4. Plug in the Values and Calculate:**V₂ = (200 kPa * 4.000 x 10³ L * 268.15 K) / (298.15 K * 200 kPa)V₂ = 3600 L (rounded to two significant figures, matching the initial volume's precision)**Answer:** The propane gas will occupy a volume of approximately 3600 L at -5°C.