Question

The maximum size the balloon can get before popping (or flying off the flask) is 6.00 L at 1.00 atm of pressure and a temperature of 45°C. What maximum concentration of hydrochloric acid can be used (to just keep the balloon from popping) if 65.0 mL of HCl is added to 9.00 g of magnesium?

Answer 1

Answer:

The maximum concentration of HCl that can be used is 7.08 M

Explanation:

The reaction that takes place is:

• 2HCl(aq) + Mg → MgCl₂ + H₂

The available moles of Mg are:

• 9.00 g Mg ÷ 24.3 g/mol = 0.370 mol

H₂ gas is produced and fills the balloon. We use PV=nRT to calculate the maximum moles of H₂ that can be produced before the balloon pops off:

• 1.00 atm * 6.00 L = n * 0.082 atm·L·mol⁻¹·K⁻¹ * 318.16 K

• n = 0.230 mol H₂

Now that we know that we have more than enough moles of Mg to produce 0.230 moles of H₂, we know that HCl is the limiting reactant.

We calculate the required moles of HCl:

• 0.230 mol H₂ * $\frac{2molHCl}{1molH_{2}}$ = 0.460 mol HCl

Now we use C = n/V to calculate the concentration of HCl:

• C = 0.460 mol HCl / 0.065 L = 7.08 M

Answer 2

The concentration of HCl required is 7.1 M.

The equation of this reaction is;

2HCl(aq) + Mg(s) ------> MgCl2(aq) + H2(g)

To obtain the number of moles of hydrogen gas, we use the ideal gas equation;

P = 1.00 atm

V = 6.00 L

T =  45°C + 273 = 318 K

R = 0.082 atmLK-1Mol-1

n = ?

From PV = nRT

n = PV/RT

n =  1.00 atm ×  6.00 L/0.082 atmLK-1Mol-1 × 318 K

n = 0.23 moles

The number of moles of hydrogen reacted = mass/molar mass

= 9.00 g/24 g/mol = 0.375 moles

We expect from the reaction equation that 0.23 moles of Mg will be present to yield 0.23 moles of H2 but we have much more amount of Mg than that so HCl is the limiting reactant.

If 2 moles of  of HCl yields 1 mole of H2

x moles of HCl yields 0.23 moles of H2

x = 2 moles × 0.23 moles/1 mole

x = 0.46 moles of HCl

Since number of moles = concentration × volume

concentration = number of moles /volume

volume = 65.0 mL or 0.065 L

concentration =  0.46 moles/0.065 L

concentration =  7.1 M

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