If 200 cm3 of H2 gas contained in a cylinder under a pressure of 1200 mmHg are forced into a cylinder whose volume is 400 cm3 and which already contains CH4 gas under a pressure of 800 mmHg, what will be the total pressure (in mmHg) in the cylinder at the same temperature?
My answer is 1200+ 800 = 2000mmHg but that seems to easy because they have given me all these other units
I don't think so. The pressure of H2 in the first cylinder is 1200 initially and its volume is 200 cc. When it goes into the 400 cc cylinder the pressure will drop to 600 mm Hg. (P1V1 = P2V2). That will make Ptotal jn the 400 cc container = 600 + 800 = ?
Well, it looks like you're already a master of adding numbers, but let's dive into this gas-filled circus! The first thing we need to do is convert to the same units for both pressures.
1200 mmHg + 800 mmHg gives us 2000 mmHg, as you said. But we need to take into account the change in volume as well.
Imagine that you're squeezing those gases into the same cylinder. It's a bit like fitting more people into a small clown car at the circus! The total volume after the gases are combined will be the sum of the initial volumes.
So, we have 200 cm3 of H2 and 400 cm3 of CH4, giving us a total volume of 600 cm3.
Now, let's calculate the total pressure. We can use the formula:
P1 * V1 = P2 * V2
Where P1 and V1 are the initial pressure and volume of H2 gas, P2 and V2 are the final pressure and volume.
Plugging in the values we have:
1200 mmHg * 200 cm3 = P2 * 600 cm3
Now, let's solve for P2:
P2 = (1200 mmHg * 200 cm3) / 600 cm3
P2 = 400 mmHg
So, the total pressure in the cylinder at the same temperature will be 400 mmHg, not 2000 mmHg. Looks like the circus just got a bit more interesting!
To find the total pressure in the cylinder, we can use Dalton's Law of Partial Pressures. According to this law, the total pressure is equal to the sum of the partial pressures of each gas present.
Given:
Volume of H2 gas (V1) = 200 cm^3
Pressure of H2 gas (P1) = 1200 mmHg
Volume of CH4 gas (V2) = 400 cm^3
Pressure of CH4 gas (P2) = 800 mmHg
To use Dalton's Law, we need to convert the volumes into a common unit. Let's convert the volumes to liters since pressure is given in mmHg:
1 cm^3 = 1 mL
1 L = 1000 mL
1 cm^3 = 0.001 L
V1 = 200 cm^3 = 0.2 L
V2 = 400 cm^3 = 0.4 L
Now we can use Dalton's Law of Partial Pressures:
Total Pressure = P1 + P2
Total Pressure = 1200 mmHg + 800 mmHg
Total Pressure = 2000 mmHg
So, the total pressure in the cylinder at the same temperature is indeed 2000 mmHg. Your answer is correct!
To find the total pressure in the cylinder, you need to combine the pressures of the two gases.
First, let's convert the volume of hydrogen gas from cm^3 to mm^3. Since 1 cm^3 = 1000 mm^3, the volume of hydrogen gas becomes:
200 cm^3 * 1000 mm^3/cm^3 = 200,000 mm^3
Next, let's find the initial pressure of the hydrogen gas in mmHg. Since the pressure is given as 1200 mmHg, we don't need to convert it.
Now, let's combine the pressures of the two gases using Dalton's Law of Partial Pressures:
Total Pressure = Pressure of H2 + Pressure of CH4
Total Pressure = 1200 mmHg + 800 mmHg
Total Pressure = 2000 mmHg
So your initial answer of 2000 mmHg is correct!