A solution is prepared by dissolving 0.2222 (¡¾0.0002) g of KIO3 in 50.00 (¡¾0.05) mL.
(i) Calculate the molar mass of KIO3 with its associated uncertainty to the correct number of significant figures.
(ii) Find the molarity and its uncertainty with an appropriate number of significant figures.
(iii) Would the answer be affected significantly if the reagent were only 99.9% pure? Why or why not
Oh, chemistry! Let's break it down, my friend.
(i) To find the molar mass of KIO3, we need to add up the atomic masses of potassium (K), iodine (I), and oxygen (O). The atomic masses are K = 39.1 g/mol, I = 126.9 g/mol, and O = 16.0 g/mol. So, KIO3 has a molar mass of 39.1 + (3 * 16.0) + 126.9 = 214.1 g/mol. And its associated uncertainty would be ¡¾0.0002 g/mol. So, the molar mass of KIO3 is 214.1 (¡¾0.0002) g/mol.
(ii) Now, let's find the molarity of the solution. Molarity (M) is defined as moles of solute per liter of solution. We know that we dissolved 0.2222 g of KIO3 in 50.00 mL of solution. First, we need to convert mL to L by dividing by 1000: 50.00 mL / 1000 = 0.05000 L.
Next, we need to find the number of moles of KIO3. We can do that by dividing the mass of KIO3 by its molar mass:
moles of KIO3 = 0.2222 g / 214.1 g/mol = 0.001037 mol.
Finally, we can find the molarity by dividing moles by liters: M = 0.001037 mol / 0.05000 L = 0.02074 M.
Since the mass of the solute was given with an uncertainty of ¡¾0.0002 g, the molarity will have the same relative uncertainty. Therefore, the molarity of KIO3 is 0.02074 (¡¾0.00002) M.
(iii) Ah, the purity question! If the reagent were only 99.9% pure, it means that 0.1% of it is impurities. It might not sound like much, but when it comes to calculations, every little bit counts! It would affect our results because the impurities would contribute to the mass and therefore to the molarity calculation. So, yes, the answer would be affected significantly if the reagent were only 99.9% pure. It's always better to work with pure substances in chemistry because we want precise results without any clowns messing around, right?
(i) To calculate the molar mass of KIO3, we need to know the molar masses of each element. The molar mass of K (potassium) is 39.10 g/mol, I (iodine) is 126.90 g/mol, and O (oxygen) is 16.00 g/mol.
To calculate the molar mass of KIO3, we multiply the molar mass of each element by the number of atoms in the compound (as indicated by the subscript) and add them together:
Molar mass of KIO3 = (39.10 g/mol x 1) + (126.90 g/mol x 1) + (16.00 g/mol x 3)
= 39.10 g/mol + 126.90 g/mol + 48.00 g/mol
= 214.00 g/mol
The molar mass of KIO3 is 214.00 g/mol.
(ii) Molarity (M) is defined as moles of solute per liter of solution. To calculate the molarity, we need to convert the mass of KIO3 into moles using its molar mass.
Number of moles of KIO3 = mass of KIO3 / molar mass of KIO3
= 0.2222 g / 214.00 g/mol
= 0.0010377 mol
The volume of the solution is given as 50.00 mL. To convert this to liters, we divide by 1000:
Volume of solution = 50.00 mL / 1000
= 0.05000 L
Molarity of KIO3 = moles of KIO3 / volume of solution
= 0.0010377 mol / 0.05000 L
= 0.02075 M
To determine the uncertainty in molarity, we need to consider the uncertainties in both the mass and volume measurements:
Uncertainty in mass = 0.0002 g
Uncertainty in volume = 0.05 mL
Converting the uncertainty in volume to liters, we divide by 1000:
Uncertainty in volume = 0.05 mL / 1000
= 0.00005 L
To calculate the uncertainty in molarity, we use the formula:
Uncertainty in molarity = (uncertainty in moles) / (volume of solution)
Uncertainty in moles = uncertainty in mass / molar mass of KIO3
Uncertainty in moles = 0.0002 g / 214.00 g/mol
= 9.35 x 10^-4 mol
Uncertainty in molarity = (9.35 x 10^-4 mol) / (0.05000 L)
= 1.87 x 10^-2 M
The molarity of the solution is 0.02075 M, with an uncertainty of 1.87 x 10^-2 M.
(iii) If the reagent were only 99.9% pure, it means that 0.1% of the reagent is impure. This impurity could affect the accuracy of the molarity calculation.
To calculate the effect of impurity on molarity, we multiply the molarity by the percentage purity:
New molarity = molarity x (100% - impurity percentage)
New molarity = 0.02075 M x (100% - 0.1%)
= 0.02075 M x (99.9%)
≈ 0.02073 M
The effect of impurity is relatively small, resulting in a slightly lower molarity. However, the difference is not significant in most cases.
(i) To calculate the molar mass of KIO3, you need to determine the atomic masses of potassium (K), iodine (I), and oxygen (O), and then multiply them by the respective number of atoms in one molecule of KIO3.
- From the periodic table, the atomic masses of K, I, and O are approximately:
K = 39.10 g/mol
I = 126.90 g/mol
O = 16.00 g/mol
- In one molecule of KIO3, you have one atom of K, one atom of I, and three atoms of O. Therefore, the molar mass of KIO3 can be calculated as follows:
Molar mass of KIO3 = (1 * atomic mass of K) + (1 * atomic mass of I) + (3 * atomic mass of O)
Molar mass of KIO3 = (1 * 39.10 g/mol) + (1 * 126.90 g/mol) + (3 * 16.00 g/mol)
Molar mass of KIO3 = 39.10 g/mol + 126.90 g/mol + 48.00 g/mol
Molar mass of KIO3 = 213.00 g/mol
To determine the associated uncertainty, let's consider the given uncertainty in the mass of KIO3, which is ±0.0002 g. This uncertainty should be propagated through the calculation.
- The uncertainty in the molar mass can be calculated using the formula:
Uncertainty in the molar mass = (uncertainty in mass of KIO3 / mass of KIO3) * 100
Uncertainty in the molar mass = (0.0002 g / 0.2222 g) * 100
Uncertainty in the molar mass = 0.090% (approximately)
Therefore, the molar mass of KIO3, with its associated uncertainty, is approximately 213.00 g/mol ± 0.090 g/mol.
(ii) To find the molarity, you need to divide the mass of KIO3 by its molar mass and then divide the result by the volume of the solution in liters.
- Convert the volume of the solution from milliliters to liters:
Volume of the solution = 50.00 mL = 50.00 mL * (1 L / 1000 mL)
Volume of the solution = 0.0500 L
- Calculate the molarity using the formula:
Molarity (M) = (mass of KIO3 / molar mass of KIO3) / volume of the solution
Molarity (M) = (0.2222 g / 213.00 g/mol) / 0.0500 L
To determine the uncertainty in molarity, we consider the uncertainties in mass and volume and propagate them through the calculation.
- The uncertainty in molarity can be calculated using the formula:
Uncertainty in molarity = (relative uncertainty in mass of KIO3 + relative uncertainty in volume of the solution) * Molarity
Uncertainty in molarity = [(0.0002 g / 0.2222 g) + (0.05 mL / 50 mL)] * Molarity
Uncertainty in molarity = (0.090 + 0.10) * Molarity
Uncertainty in molarity = 0.19 * Molarity
Therefore, the molarity of the solution, with its associated uncertainty, is approximately (0.2222 g / 213.00 g/mol) / 0.0500 L ± (0.19 * Molarity).
(iii) If the reagent were only 99.9% pure, it means that only 99.9% of the mass is actually KIO3, and the remaining 0.1% could be impurities or other compounds. This would affect the accuracy of the molarity calculation.
To factor in the purity of the reagent, you would need to adjust the mass of KIO3 used in the calculation. Instead of using the given mass (0.2222 g), you would use the actual mass of pure KIO3 present in the sample.
For example, if the reagent is 99.9% pure, the mass of pure KIO3 in the sample would be 0.999 * 0.2222 g. This adjustment would result in a slightly lower molarity value, reflecting the lower amount of actual KIO3 in the solution.
Therefore, the answer would be affected if the reagent were only 99.9% pure, as it would lead to a slightly lower molarity value due to the lower amount of the desired compound.