A gas has a volume of 46.0 L when the temperature is 400. K. When the temperature changes to 500. K, what is the new volume, if there is no change in pressure or amount of gas?
Express your answer using three significant figures.
Using the ideal gas law, we know that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. Since the pressure and amount of gas are not changing, we can rewrite the equation as V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature. Let's plug in the given values:
V1 = 46.0 L
T1 = 400 K
T2 = 500 K
V1/T1 = V2/T2
46.0/400 = V2/500
Cross-multiplying:
400V2 = 23,000
Dividing both sides by 400:
V2 = 57.5 L
Rounding to three significant figures, the new volume is 57.5 L.
According to Charles's Law, the volume of a gas is directly proportional to its temperature when pressure and amount of gas remain constant. The equation can be written as:
V1 / T1 = V2 / T2
Where:
V1 = initial volume (46.0 L)
T1 = initial temperature (400 K)
V2 = final volume (unknown)
T2 = final temperature (500 K)
To find the final volume, we can rearrange the equation:
V2 = (V1 * T2) / T1
Substituting in the given values:
V2 = (46.0 L * 500 K) / 400 K
V2 = 57.5 L
Therefore, the new volume, when the temperature changes to 500. K with no change in pressure or amount of gas, is approximately 57.5 L.
To find the new volume of the gas when the temperature changes, we can use the combined gas law formula, which relates the initial and final conditions of temperature, volume, and pressure:
(P1 x V1) / T1 = (P2 x V2) / T2
Where:
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 this case, we know that the pressure and amount of gas remain constant, so we can simplify the formula to:
V1 / T1 = V2 / T2
Substituting the given values into the formula:
V1 = 46.0 L
T1 = 400 K
T2 = 500 K
We can rearrange the formula to solve for V2:
V2 = (V1 x T2) / T1
Now we can plug in the values:
V2 = (46.0 L x 500 K) / 400 K
V2 = 57.5 L
Therefore, the new volume of the gas, when the temperature changes to 500 K, is approximately 57.5 L (rounded to three significant figures).