First, lets start with what we're given.
12.2g of MnO2, with a molecular weight of 86.9368
70 mL of 2.5M HCl
The first thing we should always do is to convert everything to moles.
To do this starting from mass, we divide the mass by the molar mass:
12.2g / 86.9368g/mol = 0.140332 mol
To do this given volume and molarity, we multiply the two together, making sure we convert mL to L first.
70 mL / 1000 mL = 0.07 L
(0.07 L) * (2.5 mol/L) = 0.175 mol
Next, we need to determine which of these are the limiting reactant. To do that, we divide the number of moles that we start with by the coefficient in the balanced chemical equation. In this case:
0.140332 mol of MnO2 / 1 mol of MnO2 required per reaction = 0.140332 moles of reactions possible
0.175 mol of HCl / 4 mol of HCl required per reaction = 0.04375 moles of reactions possible.
Through this, we can see that we will run out of HCl first, since a fewer number of reactions are possible with what we're given.
Now, let's address the question at hand. We are looking for a volume of chlorine based on the theoretical yield. We know based on the previous step that this reaction only has enough reactant to occur 0.04375 times. So, how much chlorine is that?
Based on the chemical equation, we produce 1 mol of Cl2 per mole of reaction. Thus, we multiply the number of reactions by the number of moles produced.
(0.04375 moles of reactions)*(1 mole of Cl2 produced per reaction) = 0.04375 moles of Cl2
But we don't care about moles, we are trying to get to liters. Here, we need to make an assumption that this is an ideal gas, so we can employ the equation PV=nRT.
Where P is the pressure, V is the volume (unknown), n is the number of moles, R is the ideal gas constant (0.0820574 L atm/mol K), and T is temperature in Kelvin (K = C + 273.15).
We can solve from here, since we know everything except V.
P = 0.971 atm (given)
V = unknown
n = 0.04375 mol
R = 0.0820574 L atm/mol K (constant)
T = 351.35 (78.2 + 273.15)
We can solve for V by dividing both sides of the ideal gas law by P, resulting in:
V = nRT/P
Plugging in our numbers:
V = (0.04375 mol) * (0.0820574 L atm/mol K) * (351.35 K) / (0.971 atm) = 1.299022093
We have our number, but what are our units? The standard unit for volume is Liters (L).
So, are answer is 1.299022093 Liters.
However, we aren't done. We need to pay attention to significant figures. So, from all of our given values, which value has the least amount of sig figs? This would be 2.5M HCl. This value only has two sig figs. Thus, we need to round our answer to that number.
So, our final answer becomes 1.3 Liters
