To solve this problem, we can use the law of conservation of mass, which states that the mass of the reactants must equal the mass of the products in a chemical reaction.
Given data:
- Mass of [tex]\( AB \)[/tex] is 15 g
- Mass of [tex]\( BD \)[/tex] is 10 g
- Total mass of the products [tex]\( AC \)[/tex] and [tex]\( CD \)[/tex] is 50 g.
First, calculate the total mass of the reactants:
[tex]\[ \text{Total mass of reactants} = \text{mass of } AB + \text{mass of } BD = 15 \text{ g} + 10 \text{ g} = 25 \text{ g} \][/tex]
Since the law of conservation of mass holds, the total mass of the reactants (25 g) should equal the total mass of the products. Therefore, the remaining mass for the products [tex]\(AC\)[/tex] and [tex]\(CD\)[/tex] is:
[tex]\[ \text{Total mass of products} - \text{Mass of reactants} = 50 \text{ g} - 25 \text{ g} = 25 \text{ g} \][/tex]
The remaining 25 g is the combined mass of [tex]\( AC \)[/tex] and [tex]\( CD \)[/tex]. Now we need to determine which option correctly distributes this 25 g between [tex]\( AC \)[/tex] and [tex]\( CD \)[/tex].
Given the options:
1. The amount of [tex]\( CD \)[/tex] is 40 g, and the amount of [tex]\( AC \)[/tex] is 35 g.
2. The amount of [tex]\( CD \)[/tex] is 35 g, and the amount of [tex]\( AC \)[/tex] is 40 g.
3. The amounts of [tex]\( CD \)[/tex] and [tex]\( AC \)[/tex] would be the same (each would be 12.5 g).
4. The amount of [tex]\( CD \)[/tex] and [tex]\( AC \)[/tex] is undetermined.
We can test each option to see which ones fit the remaining mass of 25 g:
1. If [tex]\( CD \)[/tex] is 40 g and [tex]\( AC \)[/tex] is 35 g:
- Total mass = 40 g + 35 g = 75 g (This exceeds the remaining 25 g, so this option is incorrect).
2. If [tex]\( CD \)[/tex] is 35 g and [tex]\( AC \)[/tex] is 40 g:
- Total mass = 35 g + 40 g = 75 g (This also exceeds the remaining 25 g, so this option is incorrect).
3. If the amounts of [tex]\( CD \)[/tex] and [tex]\( AC \)[/tex] are the same (each would be 12.5 g):
- Total mass = 12.5 g + 12.5 g = 25 g (This fits the remaining mass exactly, so this option is correct).
The correct answer is:
The amount of [tex]\( CD \)[/tex] and [tex]\( AC \)[/tex] would be the same, with each being 12.5 g.
