Help with these two please.
105. A radioactive metal atom decays (goes to another kind of atom) by emitting an alpha particle (He+2 ion). The alpha particles are collected as helium gas. A sample of helium with a volume of 12.05 mL was obtained at 765 mmHg and 23 Degrees C. How many atoms decayed during the period of the experiment?
108. A hydrocarbon gas has a density of 1.22 g/L at 20 degrees C and 1.00 atm. An analysis gives 80.0% C and 20.0% H. What is the molecular formula?
105. A radioactive metal atom decays (goes to another kind of atom) by emitting an alpha particle (He+2 ion). The alpha particles are collected as helium gas. A sample of helium with a volume of 12.05 mL was obtained at 765 mmHg and 23 Degrees C. How many atoms decayed during the period of the experiment?
Can't you use PV = nRT, solve for n mols He, change that to molecules He. Won't that be the number of atoms that decayed; that is, 1 atom He for each atom of the radioactive material that decayed?
108. A hydrocarbon gas has a density of 1.22 g/L at 20 degrees C and 1.00 atm. An analysis gives 80.0% C and 20.0% H. What is the molecular formula?
Take 100 g sample which gives you
80 g C
20 g H.
Convert to mols C and mols H.
Take the ratio and find the empirical formula. I assume you know how to do that. Then use PV = nRT but plug density instead of n and V. If you substitute g/molar mass for n and grams/v for density, you get P*molar mass = density x R*T.
That will give you the approximate molar mass, divide by the empirical molar mass to get a number,round to the nearest whole number, and use that as a multiplier x the empirical formula to arrive at the molecular formuls.
Sure, I can help you with these two questions. Let's start with question 105.
105. To find the number of atoms that decayed during the experiment, we need to use the Ideal Gas Law, which states that the number of moles of a gas can be calculated using the formula:
n = PV / RT
where:
n = number of moles
P = pressure (in atm)
V = volume (in liters)
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, we need to convert the given volume from milliliters to liters:
V = 12.05 mL = 12.05 / 1000 L
Next, we need to convert the given temperature from Celsius to Kelvin:
T = 23°C + 273.15
Now, we have all the values needed to calculate the number of moles (n) using the Ideal Gas Law.
After calculating n, we need to remember that one mole of a gas contains Avogadro's number of atoms, which is approximately 6.022 x 10^23.
So, to find the number of atoms that decayed, you need to multiply the number of moles (n) by Avogadro's number.
Now let's move on to question 108.
108. To find the molecular formula of a hydrocarbon gas, we need to determine the empirical formula first. The empirical formula gives the simplest ratio of atoms in a compound.
Given that the hydrocarbon gas consists of 80.0% carbon and 20.0% hydrogen, we can assume a 100g sample of the compound. This means we have 80g of carbon and 20g of hydrogen.
Next, we need to convert the masses of carbon and hydrogen to moles. To do this, divide the given masses by their respective molar masses. The molar mass of carbon is approximately 12.01 g/mol, and the molar mass of hydrogen is approximately 1.01 g/mol.
After finding the number of moles for each element, divide both values by the smaller of the two to get the ratio of the elements. Round the ratio to the nearest whole numbers to obtain the empirical formula.
To find the molecular formula, we then need to know the molar mass of the compound. This information is not given in the question, so we cannot determine the exact molecular formula with the given data. However, you can provide the molar mass, and I can assist you further in determining the molecular formula.
I hope that helps! Let me know if you need any further explanation or if you have any other questions.