A gas occupies 4.57 L at 330 K. What is its volume at 375 K? a 8.24 L b 6.74 L c 5.19 L d 4.02 L
The volume of a gas is directly proportional to its temperature when pressure is held constant. We can use the formula:
V₁/T₁ = V₂/T₂
Where V₁ and T₁ are the initial volume and temperature, and V₂ and T₂ are the final volume and temperature.
Plugging in the values:
V₁ = 4.57 L
T₁ = 330 K
T₂ = 375 K
V₂/T₂ = V₁/T₁
V₂ = (V₁/T₁) * T₂
V₂ = (4.57 L / 330 K) * 375 K
V₂ ≈ 5.19 L
Therefore, the volume of the gas at 375 K is approximately 5.19 L. So the correct answer is c) 5.19 L.
To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature of the gas in Kelvin
In this case, we are given that the gas occupies 4.57 L at a temperature of 330 K.
To find the volume of the gas at 375 K, we need to keep everything else constant and change only the temperature.
Let's use the formula:
V1 / T1 = V2 / T2
Where:
V1 is the initial volume (4.57 L)
T1 is the initial temperature (330 K)
V2 is the final volume (unknown)
T2 is the final temperature (375 K)
Rearranging the equation, we have:
V2 = (V1 * T2) / T1
Substituting the values, we get:
V2 = (4.57 L * 375 K) / 330 K
Calculating this gives us:
V2 = 5.19 L
Therefore, the volume of the gas at 375 K is 5.19 L. The correct answer is c) 5.19 L.
To solve this problem, we can use the combined gas law equation:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures (which are not given in this problem),
V₁ and V₂ are the initial and final volumes (V₁ = 4.57 L),
and T₁ and T₂ are the initial and final temperatures (T₁ = 330 K, T₂ = 375 K).
Since the pressure remains constant in this problem, we can simplify the equation:
V₁ / T₁ = V₂ / T₂
Now we can plug in the values:
4.57 L / 330 K = V₂ / 375 K
To solve for V₂, we can cross-multiply and divide:
V₂ = (4.57 L × 375 K) / 330 K
V₂ = 5.19 L
Therefore, the volume of the gas at 375 K is 5.19 L. Therefore, the correct answer is option c) 5.19 L.