If 200 g. of an unknown metal oxide, M2O3, upon reaction with chlorine yields 376 g of M2Cl2, then the metal M is:
a. Indium
b. Aluminum
c. Gallium
d. Silicon
e. boron
To determine the metal M in the reaction, we need to calculate the molar masses of the given compounds and use stoichiometry.
First, let's calculate the molar mass of M2Cl2. The molar mass of chlorine (Cl) is approximately 35.45 g/mol, and there are two chloride ions in M2Cl2. Therefore, the molar mass of M2Cl2 is 70.90 g/mol.
Next, let's calculate the molar mass of M2O3. The molar mass of oxygen (O) is approximately 16.00 g/mol, and there are three oxygen atoms in M2O3. Therefore, the molar mass of M2O3 is 2xM + 3x16.00 g/mol.
Now, let's set up a ratio using the given masses:
200 g M2O3 / (2xM + 3x16.00 g/mol) = 376 g M2Cl2 / 70.90 g/mol
Simplifying the equation:
200 / (2xM + 48.00) = 376 / 70.90
Cross-multiplying and further simplifying:
(2xM + 48.00) x 376 = 70.90 x 200
752xM + 18048 = 14180
752xM = 14180 - 18048
752xM = -3876
Finally, solving for x (M):
M = -3876 / 752
After evaluating the equation, we find that the value of M is negative. However, in chemistry, we are dealing with positive values for molar mass and atomic masses. Thus, there must be an error in the given values or equation.
In conclusion, based on the calculations, there seems to be an error in the given information. None of the answer choices (a. Indium, b. Aluminum, c. Gallium, d. Silicon, e. boron) can be determined without accurate data.