Magnesium metal reacts with hydrochloric acid to form magnesium chloride and hydrogen gas. Suppose we react an excess of magnesium metal with 20.0 mL of a 3.00 M solution of hydrochloric acid and collect all of the hydrogen in a balloon at 25°C and 1.00 atm. What is the expected volume of the balloon?
Group of answer choices
0.734 L
22.4 L
1.34 L
1.47 L
0.672 L
To find the expected volume of the balloon, we need to use the ideal gas law equation: PV = nRT.
First, let's find the number of moles of hydrogen gas produced in the reaction.
From the balanced chemical equation, we can see that 1 mole of magnesium metal produces 1 mole of hydrogen gas.
Since we have an excess of magnesium metal, the number of moles of hydrogen gas is equal to the number of moles of hydrochloric acid.
To find the number of moles of hydrochloric acid:
moles HCl = volume of HCl solution (in L) x concentration of HCl solution (in M)
moles HCl = 0.020 L x 3.00 M
moles HCl = 0.060 mol
Since the balanced chemical equation tells us that 1 mole of magnesium metal reacts to produce 1 mole of hydrogen gas, we know that there are 0.060 moles of hydrogen gas.
Now, let's find the volume of the balloon using the ideal gas law equation:
P = 1.00 atm (given)
V = unknown
n = 0.060 mol
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
T = 25°C = 298 K (converted to Kelvin)
PV = nRT
V = (nRT) / P
V = (0.060 mol x 0.0821 L·atm/(mol·K) x 298 K) / 1.00 atm
V = 1.34 L
Therefore, the expected volume of the balloon is 1.34 L. The correct answer choice is 1.34 L.