Please help me with this problem
Avogadro's Law
A chemical reaction occuring in a cylinder equipped with a movable piston produces 0.58 mol of gaseous product. If the cylinder contained 0.11 mol of gas before the reaction and had an initial volume of 2.11L, what was its volume after the reaction?
Did temperature change? I assume it is isopressure.
If temperature did not change, and pressure was constant, then the volume after the reaction is in proportion to the mole change, ie, .58/.11 * 2.11 dm^3
Avagradros law: equal volumes of gases (same temp, pressure) contain equal numbers of molecules. If the number of molecules changes, the volume changes accordingly.
The volume is proportional to the number of moles present, once you allow the products to return to the original temperature. The movable piston maintains a constant pressure.
Let V be the final volume.
V/2.11 liters = (0.58+0.11)/0.11 = 6.27
V = 13.2 liiters
To solve this problem, we can make use of Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
Let's break down the problem step by step:
1. Start by writing down the given information:
- Initial volume of the cylinder: 2.11 L
- Initial amount of gas in the cylinder: 0.11 mol
- Amount of gas produced by the chemical reaction: 0.58 mol
2. Since the volume of the gas changes, we need to apply Avogadro's Law to find the final volume. According to Avogadro's Law, the ratio of the volumes is equal to the ratio of moles:
(Initial volume) / (Final volume) = (Initial moles) / (Final moles)
Let's assign variables to the unknowns:
- Final volume of the cylinder: V2
- Final amount of gas in the cylinder: n2 (which is the sum of initial and produced moles)
The equation becomes:
2.11 L / V2 = 0.11 mol + 0.58 mol / n2
3. Rearrange the equation to solve for V2:
V2 = (2.11 L * n2) / (0.11 mol + 0.58 mol)
4. Substitute the values we have:
n2 = 0.11 mol + 0.58 mol
n2 = 0.69 mol
V2 = (2.11 L * 0.69 mol) / (0.11 mol + 0.58 mol)
V2 = (2.11 L * 0.69 mol) / 0.69 mol
V2 = 2.11 L
Therefore, the volume of the cylinder after the reaction is still 2.11 liters.