The useful metal manganese can be extracted from the mineral rhodochrosite by a two-step in the first step, manganese(ii) carbonate and oxygen react to form manganese(iv) oxide and carbon dioxide: 2mnco3 + o2=2mno2 + 2co2in the second step, manganese(iv) oxide and aluminum react to form manganese and aluminum oxidide: 3mno2 + 4al = 3mn + 2al2o3 suppose the yield of the first step is 65.% and the yield of the second step is 80.%. calculate the mass of manganese(ii) carbonate required to make 8.0kg of manganese. be sure your answer has a unit symbol, if needed, and is rounded to 2 significant digits.

33 kg

Explanation:

Let's consider the two steps to obtain manganese.

Step 1: 2 MnCO₃ + O₂ = 2 MnO₂ + 2 CO₂

Step 2: 3 MnO₂ + 4 Al = 3 Mn + 2 Al₂O₃

The molar mass of Mn is 54.94 g/mol. The moles represented by 8.0 kg of Mn are:

8.0 × 10³ g × (1 mol / 54.94 g ) = 1.5 × 10² mol

In Step 2, the real yield of Mn is 1.5 × 10² mol and the percent yield is 80%. The theoretical yield is:

1.5 × 10² mol (Real) × (100 mol (Theoretical) / 80 mol (Real)) = 1.9 × 10² mol

According to Step 2, the molar ratio of Mn to MnO₂ is 3:3. The moles of MnO₂ are 3/3 × 1.9 × 10² mol = 1.9 × 10² mol

In Step 1, the real yield of MnO₂ is 1.9 × 10² mol and the percent yield is 65%. The theoretical yield is:

1.9 × 10² mol (Real) × (100 mol (Theoretical) / 65 mol (Real)) = 2.9 × 10² mol

According to Step 1, the molar ratio of MnO₂ to MnCO₃ is 2:2. The moles of MnCO₃ are 2/2 × 2.9 × 10² mol = 2.9 × 10² mol

The molar mass of MnCO₃ is 114.95 g/mol. The mass of MnCO₃ represented by 2.9 × 10² mol is:

2.9 × 10² mol × (114.95 g/mol) = 3.3 × 10⁴ g = 33 kg

Answer : The mass of required are, 35 kg

Explanation :

First we have to calculate the mass of .

The first step balanced chemical reaction is:

Molar mass of = 115 g/mole

Molar mass of = 87 g/mole

Let the mass of be, 'x' grams.

From the balanced reaction, we conclude that

As, of react to give of

So, of react to give of

And as we are given that the yield produced from the first step is, 65 % that means,

The mass of obtained = 0.4542x g

Now we have to calculate the mass of .

The second step balanced chemical reaction is:

Molar mass of = 87 g/mole

Molar mass of = 55 g/mole

From the balanced reaction, we conclude that

As, of react to give of

So, of react to give of

And as we are given that the yield produced from the second step is, 80 % that means,

The mass of obtained = 0.2296x g

The given mass of Mn = 8.0 kg = 8000 g     (1 kg = 1000 g)

So, 0.2296x = 8000

x = 34843.20 g = 34.84 kg = 35 kg

Therefore, the mass of required are, 35 kg