Bulb A is 100 mL and contains Helium at 1 atm. Bulb B is 500 mL and contains Argon at 2 atm. The bulbs are connected together by a valve. What is the pressure of gas A after the valves are opened? (assume constant temperature)
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The long way is easier to explain but there is a shorter route.
Long way.
He. Use PV = nRT and solve for n. Use any convenient T.
Ar. Use PV = nRT and solve for n. use same T.
Add n He to n Ar and plug into PV = nRT. use same T as before and for V use the combined volumes.
To find the pressure of gas A after the valves are opened, we will use the principle of the ideal gas law, which states that the product of the pressure (P), volume (V), and number of moles (n) of a gas is directly proportional to its temperature (T).
The ideal gas law equation is given as:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since we are assuming constant temperature, the equation can be simplified to:
P1V1 = P2V2,
where P1 and V1 are the initial pressure and volume of gas A (Helium), and P2 and V2 are the final pressure and volume of gas A after the valves are opened.
Given:
Bulb A: V1 = 100 mL = 0.1 L (converted from milliliters to liters)
P1 = 1 atm
Bulb B: V2 = 500 mL = 0.5 L (converted from milliliters to liters)
P2 = 2 atm
Using the equation P1V1 = P2V2, we can rearrange it to solve for P2:
P2 = (P1V1) / V2
Plugging in the values:
P2 = (1 atm * 0.1 L) / 0.5 L
Calculating:
P2 = 0.2 atm
Therefore, the pressure of gas A (Helium) after the valves are opened is 0.2 atm.