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Why does his teacher ask him to balance the equation by including the correct coefficient

If i initially have a gas at a pressure of 12 atm, a volume of 23 liters, and a temperature of 200 k, and then i raise the pressure to 14 atm and increase the temperature to 300 k, what is the new volume of the gas?

Modern pennies are composed of zinc coated with copper. a student determines the mass of a penny to be 2.482 g and then makes several scratches in the copper coaling (to expose the underlying zinc). the student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the hcl (the copper remains undissolved): zn(s) + 2 hcl(aq) → h2(g) + zncl(aq)the student collects the hydrogen produced over water at 25 °c. the collected gas occupies a volume of 0.899 l at a total pressure of 79 j mmhg. calculate the percent zinc (by mass) in the penny. (assume that all the zn in the penny dissolves.)