To solve this problem, we need to understand the relationship between the mass of magnesium and the mass of copper that can be produced based on the given chemical reaction and the ratio of their atomic weights.
The chemical reaction given is:
[tex]\[ \text{Mg} + \text{Cu(NO}_3\text{)}_2 \rightarrow \text{Cu} + \text{Mg(NO}_3\text{)}_2 \][/tex]
This reaction tells us that one atom of magnesium (Mg) reacts with one molecule of copper(II) nitrate ([tex]\( \text{Cu(NO}_3\text{)}_2 \)[/tex]) to produce one atom of copper (Cu) and one molecule of magnesium nitrate ([tex]\( \text{Mg(NO}_3\text{)}_2 \)[/tex]).
Now, we are given that the ratio of the atomic weight of copper (Cu) to the atomic weight of magnesium (Mg) is about 2.61. This means that one unit of magnesium mass can produce 2.61 units of copper mass.
Given the initial mass of the magnesium, let's assume it is 1 unit (this could be in grams, kilograms, etc., but the calculation remains scale-invariant).
Step-by-step solution:
1. Identify the initial mass of magnesium:
Suppose the initial mass of the magnesium strip is 1 unit.
2. Understand the weight ratio:
Given that the ratio of the atomic weight of copper (Cu) to the atomic weight of magnesium (Mg) is about 2.61. This implies:
[tex]\[
\frac{\text{Mass of Cu}}{\text{Mass of Mg}} = 2.61
\][/tex]
3. Calculate the mass of copper produced:
To find the mass of copper that can be produced from the initial mass of magnesium, we multiply the initial mass of magnesium by the ratio of the atomic weights:
[tex]\[
\text{Mass of Cu produced} = \text{Initial mass of Mg} \times \text{Ratio of atomic weight}
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Mass of Cu produced} = 1 \times 2.61 = 2.61 \text{ units}
\][/tex]
Therefore, the mass of copper that can be produced from 1 unit of magnesium is 2.61 units.
This step-by-step solution allows us to conclude that based on the given ratio and the initial mass of magnesium, the mass of copper that can be produced is 2.61 units.
