A graduated tube, sealed at the upper end has a mercury leveling bulb connected to the lower end. the gas volume is 25.ml, when the mercury level is the same in both ends. the barometric pressure is 732 mm Hg. What is the gas volume when the mercury level on the open side is 10 cm above the mercury level in the closed side?
21.99 ml
p1v1=p2v2
p1=732mmhg
v1=25ml
p2=732+100=832mmhg
v2=?
732*25=832*v2
v2=21.99
Ana - if the mercury rises in the open end, then it must drop in the closed end. Since the closed end presumably holds the 25 ml of gas, the volume would have to increase, it couldn't be a smaller number like 21.99. It all depends on how you picture this contraption I guess.
To find the gas volume when the mercury level on the open side is 10 cm above the mercury level in the closed side, we can use Boyle's Law. Boyle's Law states that the pressure exerted by a gas is inversely proportional to its volume, assuming constant temperature.
Here's how you can calculate the gas volume:
1. Convert the given barometric pressure to the same unit as the mercury level. In this case, we have 732 mm Hg, so we convert it to cm by dividing by 10:
732 mm Hg / 10 = 73.2 cm Hg
2. Determine the difference in mercury levels between the open side and the closed side.
The difference is 10 cm.
3. Subtract the difference in mercury levels from the barometric pressure to get the pressure on the gas in the graduated tube:
73.2 cm Hg - 10 cm = 63.2 cm Hg
4. Set up a proportion using Boyle's Law:
Pressure1 * Volume1 = Pressure2 * Volume2
We know that the volume when the mercury levels are the same (Volume1) is 25 mL.
Let's assume Volume2 is the unknown gas volume we need to find.
The pressure when the mercury levels are the same (Pressure1) is the barometric pressure, which is 73.2 cm Hg.
The pressure when the mercury level on the open side is 10 cm above the mercury level in the closed side (Pressure2) is 63.2 cm Hg.
Plugging the known values into the equation and solving for Volume2:
73.2 cm Hg * 25 mL = 63.2 cm Hg * Volume2
Rearranging the equation, we get:
Volume2 = (73.2 cm Hg * 25 mL) / 63.2 cm Hg
5. Calculate the gas volume by plugging in the values and evaluating the equation:
Volume2 = (73.2 cm Hg * 25 mL) / 63.2 cm Hg
Volume2 ≈ 28.97 mL
Therefore, the gas volume when the mercury level on the open side is 10 cm above the mercury level in the closed side is approximately 28.97 mL.