Question

Element \(\Lambda\) (atomic weight \(12.01)\) and element \(\mathrm{B}\) (atomic weight 16 ) combine to form a new substance \(\mathrm{X}\). If two moles of \(\mathrm{B}\) combines with one mole of \(\Lambda\), then the weight of one mole of \(\mathrm{X}\) is (1) \(28.01 \mathrm{~g}\) (2) \(44.01 \mathrm{~g}\) (3) \(40.02 \mathrm{~g}\) (4) \(56.02 \mathrm{~g}\)

Short answer

44.01 g

Step-by-step solution

- Determine the number of moles for each element in substance X

The problem states that two moles of element B combine with one mole of element \(\Lambda\) to form one mole of substance X.

- Find the atomic weight contribution for each element

Element \(\Lambda\) has an atomic weight of 12.01, and element B has an atomic weight of 16. Since one mole of \(\Lambda\) is combined with two moles of B, the total atomic weight contribution from \(\Lambda\) is 12.01 and from B is \(2 \times 16 = 32\).

- Calculate the total weight of one mole of substance X

Add the atomic weight contributions from \(\Lambda\) and B to get the total weight of one mole of substance X: \(12.01 + 32 = 44.01\) g

Key concepts

stoichiometry

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in a chemical reaction. In this exercise, stoichiometry is used to determine the amount of each element that combines to form a new substance, X.
The given problem states that one mole of element \(\text{Λ}\) (with an atomic weight of 12.01) combines with two moles of element B (with an atomic weight of 16). By analyzing these quantities, we can understand how the elements react on a mole-to-mole basis.
To solve such problems, we use stoichiometry to find out how the molar quantities translate to actual weights. This helps in calculating the final weight of the compound formed.
Understanding stoichiometry ensures that we can correctly measure the proportions of substances involved in reactions, leading us to accurate outcomes and reducing errors.

atomic weight

Atomic weight, often known as atomic mass, is the weight of an atom of a chemical element. It is usually measured in atomic mass units (amu), which are based on the carbon-12 isotope.
In this exercise, the atomic weight of element \(\text{Λ}\) is given as 12.01, and for element B, it is 16. The atomic weights tell us how much one mole of each element weighs.
When combining elements to form a compound, such as substance X in our problem, knowing the atomic weights allows us to calculate the compound’s total weight. For example, one mole of \(\text{Λ}\) contributes 12.01 grams, and two moles of B contribute 2 \times\ 16 grams, resulting in a total of 32 grams from B.
By summing these contributions, we determine that one mole of the new substance X weighs 44.01 grams.

mole concept

The mole concept is a fundamental principle in chemistry that relates the amount of a substance to the number of particles it contains. One mole is defined as containing exactly 6.022 \times\ 10^23 particles (atoms, molecules, ions, etc.).
In this exercise, we use the mole concept to combine one mole of element \(\text{Λ}\) with two moles of element B to form one mole of substance X. This illustrates how moles help in comparing amounts of different substances involved in the same reaction.
Understanding the mole concept allows us to convert between the mass of a substance and the number of moles, facilitating the calculation of overall weight in chemical reactions. For instance, knowing that one mole of \(\text{Λ}\) weighs 12.01 grams and two moles of B weigh 32 grams makes it easy to find the total weight of the resulting compound X, which is 44.01 grams.