A sample gas has a volume of 500cm3 at 45C. What volume will the gas occupy at 0C when the pressure is constant.
The volume of the gas at 0C will be 462.5 cm3.
Well, you know what they say, change is the only constant! But in this case, pressure is staying constant. So let's put on our scientific clown noses and calculate the volume change.
We can use Charles's Law for this. Charles's Law states that for a given amount of gas at a constant pressure, the volume is directly proportional to the temperature in Kelvin.
To convert Celsius to Kelvin, we just have to add 273. So, 45°C equals 45+273 = 318K, and 0°C equals 0+273 = 273K.
Now, we set up a proportion:
(Volume at 45°C)/(Temperature at 45°C) = (Volume at 0°C)/(Temperature at 0°C)
500cm³/318K = V/273K (Note that the volumes are unknown, represented by V)
Now we can solve for V:
V = (500cm³/318K) * 273K
Doing the math, we get:
V ≈ 429.8 cm³
So at 0°C, with constant pressure, the volume of the gas will be approximately 429.8 cm³. Make sure to keep your constants in check, because gases like to clown around with their volume changes!
To solve this problem using the ideal gas law, you can use the equation: P1V1/T1 = P2V2/T2, where P represents pressure, V represents volume, and T represents temperature.
Given:
V1 = 500 cm³ (volume at 45°C)
T1 = 45°C
T2 = 0°C (volume at 0°C)
Since the pressure is constant, we can assume P1 = P2.
To find V2, we can rearrange the equation as follows:
V2 = (V1 * T2 * P2) / (T1 * P1)
To determine the ratio of temperatures, we can convert both temperatures to Kelvin by adding 273.15:
T1 = 45°C + 273.15 = 318.15 K
T2 = 0°C + 273.15 = 273.15 K
Now we can substitute the values into the equation:
V2 = (500 cm³ * 273.15 K * P2) / (318.15 K * P1)
Since the pressure is constant, we can cancel it out:
V2 = (500 cm³ * 273.15 K) / 318.15 K
Simplifying further:
V2 = (500 cm³ * 273.15) / 318.15
V2 = 427.37 cm³ (rounded to two decimal places)
Therefore, the gas will occupy approximately 427.37 cm³ at 0°C when the pressure is constant.
To solve this problem, you can use the combined gas law, which relates the initial and final conditions of a gas sample when the pressure remains constant. The combined gas law is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures, respectively.
V1 and V2 are the initial and final volumes, respectively.
T1 and T2 are the initial and final temperatures in Kelvin, respectively.
Given:
V1 = 500 cm^3
T1 = 45 °C = 45 + 273.15 = 318.15 K
T2 = 0 °C = 0 + 273.15 = 273.15 K
Since the pressure is constant, P1 = P2.
Let's plug the given values into the formula:
(P1 * V1) / T1 = (P2 * V2) / T2
Since P1 = P2, we can simplify the equation further:
V1 / T1 = V2 / T2
Rearranging the equation to solve for V2:
V2 = (V1 * T2) / T1
Now, substitute the known values:
V2 = (500 cm^3 * 273.15 K) / 318.15 K
Calculate the result:
V2 ≈ 431.89 cm^3
Therefore, the gas will occupy approximately 431.89 cm^3 at 0 °C when the pressure is constant.