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A certain metal oxide has the formula MO where M denotes the metal. A 39.46g sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, 31.70g of the metal is left over. If O has an atomic mass of 16.00 amu, calculate the atomic mass of M and identigy the element.

For this question the answers where Atomic Mass: 65.4 amu and element: Zn

but I don't know how to solve this.

My textbook doesn't have any examples like this question.

Use proportions.

The mass of the oxide before and after reduction contain the same amount of metal. The masses are proportional to the sum of the AMU's:
(M+16)/M = 39.46/31.7
Cross multiply to get
31.7(M+16) = 39.46M
Solve for M to get
M=64.87
which lies between Cu at 63.55 and Zn at 65.39.
Margin of error required if the metal is Zn: (65.39-64.87)/65.39= 0.8%
which could be acceptable depending on the laboratory conditions.

Thank you

To solve this problem, you can follow these steps:

Step 1: Calculate the mass of oxygen that was removed.
To find the mass of oxygen, subtract the mass of the metal left over from the initial mass of the compound.
Mass of oxygen = Initial mass of compound - Mass of metal left over
Mass of oxygen = 39.46 g - 31.70 g
Mass of oxygen = 7.76 g

Step 2: Convert the mass of oxygen to moles.
To do this, divide the mass of oxygen by its atomic mass.
Number of moles of oxygen = Mass of oxygen / Atomic mass of oxygen
Number of moles of oxygen = 7.76 g / 16.00 g/mol
Number of moles of oxygen = 0.485 mol

Step 3: Determine the number of moles of metal present.
The number of moles of the metal is equal to the number of moles of oxygen because the formula for the metal oxide is MO, indicating a 1:1 ratio of metal to oxygen.
Number of moles of metal = Number of moles of oxygen

Step 4: Calculate the molar mass of the metal.
To find the molar mass of the metal, divide the mass of the metal by the number of moles.
Molar mass of metal = Mass of metal / Number of moles of metal
Molar mass of metal = 31.70 g / 0.485 mol
Molar mass of metal ≈ 65.4 g/mol

Step 5: Identify the element.
The molar mass of the metal is approximately 65.4 g/mol. By referring to the periodic table, you can determine which element has a molar mass close to this value. In this case, the element with the closest molar mass is Zinc (Zn), which has a molar mass of 65.38 g/mol.

Therefore, the atomic mass of M is 65.4 amu, and the element is Zinc (Zn).

To solve this question, you can follow these steps:

Step 1: Determine the mass of oxygen in the sample.
The initial mass of the sample is 39.46g, and the final mass of the metal left over is 31.70g. Therefore, the mass lost during heating is equal to the mass of oxygen in the sample.

Mass of oxygen = Initial mass - Final mass
Mass of oxygen = 39.46g - 31.70g
Mass of oxygen = 7.76g

Step 2: Convert the mass of oxygen to moles.
To convert the mass of oxygen to moles, divide the mass by its molar mass. The molar mass of oxygen is 16.00 g/mol.

Number of moles of oxygen = Mass of oxygen / Molar mass of oxygen
Number of moles of oxygen = 7.76g / 16.00 g/mol
Number of moles of oxygen ≈ 0.485 mol

Step 3: Determine the number of moles of metal.
Since the metal oxide has the formula MO, it means that for every mole of oxygen, there is also one mole of metal (M). This means the number of moles of metal is equal to the number of moles of oxygen.

Number of moles of metal ≈ 0.485 mol

Step 4: Calculate the atomic mass of M.
The atomic mass of M can be determined by dividing the mass of the metal (31.70g) by the number of moles of metal.

Atomic mass of M = Mass of metal / Number of moles of metal
Atomic mass of M = 31.70g / 0.485 mol
Atomic mass of M ≈ 65.4 amu

Step 5: Identify the element.
Based on the atomic mass of M (65.4 amu), you can consult the periodic table to determine the element that corresponds to this atomic mass. In this case, an atomic mass of approximately 65.4 amu corresponds to the element Zinc (Zn).

Therefore, the answer to the question is:
Atomic Mass: 65.4 amu
Element: Zinc (Zn)