How much element B would combine with 12 g of element A if 4.0 g of A combine with 10 g of B?
Understand the Problem
The question is asking for the amount of element B that will combine with a given mass of element A based on a known ratio of their combination. To solve it, we will set up a proportion using the given data to find the required mass of element B for 12 g of element A.
Answer
The mass of element B needed is \( 16 \) g.
Answer for screen readers
The mass of element B that will combine with 12 g of element A is ( 16 ) g.
Steps to Solve
- Identify the known ratio
First, determine the given ratio of elements A and B. Let's say the ratio is ( a:b ). For instance, if we know that 3 g of A reacts with 4 g of B, the ratio is ( 3:4 ).
- Set up the proportion
Next, set up a proportion using the ratio and the given mass of element A, which is 12 g. The proportion can be set up as follows:
$$ \frac{A}{B} = \frac{3}{4} $$ $$ \frac{12}{x} = \frac{3}{4} $$
Where ( x ) is the mass of element B we want to find.
- Cross-multiply to solve for ( x )
Cross-multiplying gives us:
$$ 3x = 12 \times 4 $$
- Calculate ( x )
Now, perform the multiplication on the right side:
$$ 3x = 48 $$
Next, divide both sides by 3 to isolate ( x ):
$$ x = \frac{48}{3} $$
- Find the final value of ( x )
Calculating the division gives us:
$$ x = 16 $$
The mass of element B that will combine with 12 g of element A is ( 16 ) g.
More Information
In chemical reactions, elements combine in specific ratios, which can be crucial information in stoichiometry. Knowing these ratios allows chemists to predict how much of one substance is required to react completely with another.
Tips
- Misunderstanding the ratio: Ensure the ratio is set up properly. Verify that the correct values are used to form the proportion.
- Incorrect cross-multiplication: Double-check the multiplication step to avoid calculation errors.
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