Determining volume

Question

What volume of hydrogen gas is formed at 30oC, and 950 mmHg, when 5.00g of calcium reacts with 250.0 mL of 0.700M hydrochloric acid.

Answer 1

Hi Stephen, thanks for asking this question! It has a multi-step answer so there is a lot to learn here. First, let's start off by determining the chemical reaction that is occurring. Hydrogen gas is being formed, so that will be a product. Calcium and hydrochloric acid are reacting with each other, so they will be our reactants.

Ca + HCl → H₂ + ??

Hydrogen gas is a diatomic molecule, so it has the formula H₂. This chemical reaction is incomplete and unbalanced because there is no Ca or Cl on the right-hand side. To determine the chemical formula of a compound containing Ca and Cl, use your periodic table to find the oxidation numbers to be Ca²⁺ and Cl^1-. Then, "cross them down" to find our chemical formula to be CaCl₂ (This means that for every 1 calcium atom, 2 chlorine atoms bond with it). Let's add that missing compound to our single-replacement reaction:

Ca + HCl → H₂ + CaCl₂ Let's balance this by adding some coefficients

Ca + 2 HCl → H₂ + CaCl₂ Every element has an equal number on both sides of the reaction

Step 1 is complete! We have a balanced reaction, what does it mean? It means 1 mole of Ca and 2 moles of HCl will react to produce 1 mole of hydrogen gas and 1 mole of calcium chloride. We can use this like a recipe to find out how much of our 5 g of Ca and 250 mL of 0.7M HCl will react to produce the hydrogen gas. Our next step is to figure out what those amounts are in moles (because that is how our "recipe" is measured).

Use the molar mass aka molecular weight of calcium to convert grams to moles:

5 g Ca • 1 mol Ca = 0.125 mol Ca

40 g Ca

Convert the HCl concentration measured in Molarity (mol/L) into moles:

0.25 L • 0.7 mol/L = 0.175 mol HCl

What is our limiting reactant, the "ingredient" that prevents us from making more? Remember, we need 2 times more HCl than Ca based on our molar ratio in the above reaction.

For 0.125 mol of Ca to react, we would need 0.25 mol of HCl (which we don't have)

For 0.175 mol of HCl to react, we would need 0.0875 mol of Ca.

HCl is the limiting reactant. We will use all 0.175 mol of HCl to react with only 0.0875 mol of Ca to produce 0.0875 mol of Hydrogen gas and 0.0875 mol of CaCl₂ (Following the "recipe proportions" of our chemical reaction's coefficients)

Now we know that we will be producing 0.175 mol of H₂. We can use the Ideal Gas Law, PV = nRT, to determine what that amount of gas would be under the conditions given in the problem.

R is a gas constant dependent on the units of measurement of pressure (in this case, atm)

R = 0.0821 L·atm/mol·K (notice that temperature is in Kelvin, not Celsius)

The pressure given is in mmHg instead of atm. 1 atm = 760 mmHg

950 mmHg • 1 atm = 1.25 atm

760mmHg

Now, plug in all of the variables. All units should cancel out to give the volume in Liters

(1.25 atm) V = (0.175 mol) (0.0821 L·atm/mol·K) (303K)

That was alot! Feel free to ask any additional questions if you have any.