Consider a hypothetical reaction in which A and B are reactants, and C and D are products. If 22 grams of A completely reacts with 14 grams of B to produce 9 grams of C, how many grams of D will be produced? Show all work! What law does this question demonstrate?
law of conservation of mass
MassA + MassB=MassC+MassD
massD= MassA+MassB-MassC
To solve this question, we need to use the concept of stoichiometry and the law of conservation of mass.
First, let's calculate the molar masses of A, B, and C by summing the atomic masses of their constituent atoms. The molar mass of a substance is the mass of one mole of that substance in grams.
Let's say the molar mass of A is MA, the molar mass of B is MB, and the molar mass of C is MC.
Next, we need to determine the reaction stoichiometry. From the given information, we know that 22 grams of A completely reacts with 14 grams of B to produce 9 grams of C. Using the molar masses, we can convert the masses to moles.
The number of moles of A is given by:
moles of A = (mass of A) / (molar mass of A) = 22 g / MA
Similarly, the number of moles of B is given by:
moles of B = (mass of B) / (molar mass of B) = 14 g / MB
Now, let's determine the moles of C produced in the reaction. From the balanced chemical equation, we can assume that the stoichiometric coefficient of C is 1 (since no coefficient is provided in the question). Therefore, the number of moles of C is also equal to the number of grams of C divided by its molar mass:
moles of C = (mass of C) / (molar mass of C) = 9 g / MC
Since the reaction is stoichiometric, the ratio of moles of A to moles of C must be the same as the ratio of moles of B to moles of D. Therefore, we can write:
(moles of A) / (moles of B) = (moles of C) / (moles of D)
Substituting the values we calculated earlier, we have:
(22 g / MA) / (14 g / MB) = (9 g / MC) / (moles of D)
Rearranging the equation to solve for the moles of D:
moles of D = (14 g / MB) * (9 g / MC) * (moles of A) / (22 g / MA)
Now, we can calculate the grams of D by multiplying the moles of D by its molar mass:
mass of D = (moles of D) * (molar mass of D)
By following these calculations, we can find the grams of D produced. Since the molar masses of A, B, and C are not provided in the question, the numerical result cannot be determined with the given information.
The law that this question demonstrates is the law of conservation of mass. According to this law, the total mass of the reactants must be equal to the total mass of the products in a chemical reaction.