Some Basic Concepts Of Chemistry

(A) Energy and torque:

• Energy has dimensions .
• Torque has dimensions .

(B) Force and impulse:

• Force has dimensions .
• Impulse has dimensions .

(C) Angular momentum and Planck constant:

• Angular momentum has dimensions .
• Planck constant (h) has dimensions .

(D) Elastic modulus and pressure:

• Elastic modulus has dimensions .
• Pressure has dimensions .

From the above data, Force and impulse does not have equal dimensions.

So, the correct option is (B): Force and impulse

Molar mass of Ba = 137.33 g/mol

Molar mass of C = 12.01 g/mol

Molar mass of O = 16.00 g/mol

Molar mass of BaCO₃ = 137.33 + 12.01 + 3 x 16.00 = 197.34 g/mol

Moles of BaCO₃ =

Moles of BaCO₃ = ≈ 0.05 moles

Balanced chemical equation for the decomposition of BaCO₃

The stoichiometry tells us that one mole of BaCO₃ produces one mole of CO_2.

Moles of CO₂ = Moles of BaCO₃ ≈ 0.05 moles

Now, use the ideal gas law to find the volume of CO₂ at standard temperature and pressure (STP):

The molar volume of an ideal gas at STP is 22.4 liters/mol.

Volume of CO₂ = Moles of CO₂ x Molar volume at STP

Volume of CO₂ = 0.05 moles x 22.4 liters/mole = 1.12 liters

So, the correct option is (B):

The balanced chemical equation for the production of aluminum from bauxite is:
2Al₂O₃ + 3C → 4Al + 3CO₂

The molar mass of aluminum (Al) is 27 g/mol.

270 kg of aluminum metal to be produced, which is equivalent to 270,000 grams.

Moles of Al = Mass of Al / Molar Mass of Al
Moles of Al = 270,000 g / 27 g/mol
Moles of Al = 10,000 moles

From the balanced equation, we can see that 3 moles of carbon (C) are required to produce 4 moles of aluminum (Al). Therefore, the mole ratio of C to Al is 3:4.

Now, calculating the moles of carbon required to produce 10,000 moles of aluminum:

Moles of C = (10,000 moles of Al) × (3 moles of C / 4 moles of Al)
Moles of C = 7,500 moles

Now, we need to find the mass of carbon (C) consumed:

Mass of C = Moles of C × Molar Mass of C
Mass of C = 7,500 moles × (12 g/mol)
Mass of C = 90,000 g

So, the mass of the carbon anode consumed in the production of 270 kg of aluminum metal from bauxite by the Hall process is 90,000 grams or 90 kg.

Therefore, the correct option is (D): 90 kg

The balanced chemical equation is
From the above equation, we note that 24 g Mg reacts with 16 g O₂ 
Therefore, 1.0 g Mg reacts with
However, only 0.56 g of O₂ is available.
Thus, O₂ is the limiting reagent.
16 g O₂ then reacts with 24 g Mg. 
0.56 g O₂ will react with Mg
The amount of Mg left unreacted = 1.0 - 0.84g Mg = 0.16g Mg.
Hence, Mg is present in excess and 0.16 g Mg is left behind unreacted.

So, the correct option is (A): Mg, 0.16 g