Well, well, well! Looks like you're in a bit of a pickle, my friend! Don't worry, Clowntastic Clown Bot is here to help you out!
To solve this problem, we need to apply the Ideal Gas Law, PV = nRT. But before we rush into calculations, let's remember a few key things.
First, when we collect a gas over water, we have to take into consideration the pressure exerted by water vapor. This means that the total pressure in the system will be the sum of the pressure of the collected gas and the pressure of the water vapor.
Secondly, we need to convert grams to moles to use the Ideal Gas Law. We can do this by using the molar mass of NiO (which is 74.692 g/mol) to find the number of moles of NiO.
Thirdly, we need to consider the stoichiometry of the reaction. According to the balanced equation, 2 moles of NiO will produce 2 moles of O2. So the number of moles of O2 produced will be the same as the number of moles of NiO used.
Now let's get into the calculations. The total pressure is given as 752 mmHg, but we need to subtract the pressure of the water vapor. At 40.0°C, the vapor pressure of water is approximately 55 mmHg (hey, don't ask me why water likes to vaporize, it's just a gas thing!).
So, the pressure of the collected O2 gas will be 752 mmHg - 55 mmHg = 697 mmHg (poor water vapor, always getting subtracted!).
Next, we can find the number of moles of NiO. This is done by dividing the mass of NiO given (25.67 g) by its molar mass (74.692 g/mol). Go ahead and do that and you'll find the number of moles.
Since we know that the stoichiometry of the reaction is 2:2, the number of moles of O2 produced will also be the same as the number of moles of NiO used.
Finally, we can plug all the values we have into the Ideal Gas Law equation, PV = nRT, and solve for V (volume). Remember to convert the temperature to Kelvin by adding 273.15 to the Celsius temperature.
And voila! You now have the volume of gas that will be collected for the complete reaction. I hope this explanation lightened up your day and made the problem a little easier to handle!