how would you figure this out?
if 500 mL of hydrogen are colected over water at 20 degrees c and 745 torr, what will the volume of the dry gas be at STP?
You can use (P1V1)/T1 = (P2V2)/T2
Use for P1 = 745 - vapor pressure of water at 20 degrees C (which you will find in a table--I'm sure your text has one). V1 is of course 500 mL and you are solving for V2. Don't forget to change T to Kelvin. Post your work if you get stuck.
To solve this question, you need to use the combined gas law and convert the given conditions to STP (Standard Temperature and Pressure). Here's how you would figure it out step by step:
1. Begin by identifying the variables given in the problem:
- Volume of hydrogen collected over water (vapor pressure of water included) = 500 mL
- Temperature = 20 degrees Celsius
- Pressure = 745 torr
- We need to find the volume of the dry gas at STP.
2. Convert the temperature to Kelvin since we'll be using the Kelvin scale in gas law calculations. To convert Celsius to Kelvin, add 273.15 to the temperature:
- Temperature in Kelvin = 20 + 273.15 = 293.15 K
3. Convert the pressure from torr to atmospheres (atm), which is the unit commonly used in gas law calculations. Since 1 atm is equal to 760 torr, divide the given pressure by 760:
- Pressure in atm = 745 torr / 760 torr/atm = 0.98026 atm
4. Now, apply the combined gas law with the given conditions and STP:
- Combined Gas Law formula: (P1 * V1) / (T1) = (P2 * V2) / (T2)
- Let's assign the given values:
P1 = 0.98026 atm (at 20°C and 745 torr)
V1 = 500 mL
T1 = 293.15 K (converted from 20°C)
P2 = 1 atm (STP condition)
V2 = ? (volume at STP)
T2 = 273.15 K (STP condition)
5. Rewrite the combined gas law equation with the given and unknown variables:
- (0.98026 atm * 500 mL) / (293.15 K) = (1 atm * V2) / (273.15 K)
6. Solve for V2 (volume at STP):
- Rearrange the equation to isolate V2:
V2 = [(0.98026 atm * 500 mL) / (293.15 K)] * (273.15 K / 1 atm)
- Calculate the equation:
V2 ≈ 453.07 mL
Therefore, the volume of the dry gas at STP is approximately 453.07 mL.