Calculate the number of moles in a 100-milliliter solution of HCL that reacts when 2.65 grams of zinc is added to it, giving your answer to the nearest one decimal place. Note that 𝐴 sub 𝑟 of zinc is given to 65 unified atomic mass units.
We can begin this problem by writing a balanced chemical equation for the reaction of HCL with zinc. Hydrochloric acid and zinc react via a single displacement reaction to produce zinc chloride and hydrogen gas. Be careful and ensure that the reaction is balanced by adding appropriate coefficients before continuing on with the rest of the problem.
We would like to relate 2.65 grams of zinc to moles of hydrochloric acid. Grams of one substance cannot be directly related to moles of another substance. However, two different substances can be related to one another via their molar ratio, which in the case of hydrochloric acid to zinc is two to one. This relationship comes directly from our balanced chemical equation.
In order to use our molar ratio, our zinc value in grams must be converted into moles. To do this, we will need the key equation 𝑛 equals lowercase 𝑚 over capital 𝑀, where 𝑛 represents the amount in moles, lowercase 𝑚 is the mass in grams, and capital 𝑀 is the molar mass in grams per mole. The mass of zinc used is given in the question, along with the relative atomic mass of zinc. Recognize that the molar mass of zinc has the same numerical value as the relative atomic mass but is given the unit grams per mole. We can substitute the mass and molar mass into the key equation and determine the number of moles of zinc to be 0.0408 moles.
Next, we will relate the moles of zinc to the moles of hydrochloric acid using the molar ratio. As the molar ratio is not one to one, we will need to perform a conversion. We begin the conversion process with the moles of zinc. We multiply this value by the molar ratio written as a fraction with moles of zinc in the denominator so that the units canceled out. We perform the calculation and determine the number of moles of hydrochloric acid to be 0.0816 moles. The question asks us to report our answer to the nearest one decimal place. Rounding appropriately, we get a final answer of 0.1 moles.