Can someone please help me with this Chemistry question

Question

Magnesium metal reacts with hydrochloric acid according to the following equation:

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

When 0.425 grams of magnesium was added to 150.0 mL of 1.00 M HCl in a coffee-cup calorimeter the temperature of the solution increased from 24.5 degrees Celsius to 35.3 degrees Celsius. Given that the heat capacity of the calorimeter is 125 J/degrees Celsius and that the density of the HCl solution is 1.00 g/mL, calculate the heat released per mole of magnesium.

Answer 1

You are asked to calculate the heat released (J) per mol of magnesium. Use the following equations:

ΔH_rxn = q_rxn/mol.

q_soln = m_soln x C_s,soln x ΔT

q_rxn = -q_soln

First you have to calculate the mass of the solution by using the 150 mL of HCL and the density

m_soln = 150 mL x 1.00 g/1 mL = 150 g

They gave you C_s,soln = 1.25 J/g·°C (You have 125, but it may be 1.25 and check the units as well. The units for specific heat is usually what I have written above) I will be using 1.25.

The change in temperature is T_f - T_i = 35.3 - 24.5 = 10.8°C

Now you have everything to solve for q_soln

q_soln = m_soln x C_s,soln x ΔT

150 g x 1.25 J/g·°C x 10.8 °C = 2025 J all the units cancel out except J

Now we can determine q_rxn

q_rxn = -q_soln

= -2025 J

Now we can determine the heat released (Need to calculate the moles of magnesium first)

ΔH_rxn = q_rxn/mol Mg 0.425 g Mg • 24.3g/1mol = 0.0175 mol

= -2025 J / 0.0175 mol = -1.16 x 10⁵ J/mol

If needed to get J by itself, just multiply by the moles of magnesium in the equation to cancel out moles

-1.16 x 10⁵ J/mol• 1 mol Mg = -1.16 x 10⁵ J

Answer 2

Calculate the heat released per mole of magnesium.

1. Find the energy change due to heat
2. Find the moles of magnesium
3. Divide

Heat released:

q=Cdt

q=heat change of calorimeter

C=heat capacity of calorimeter = 125 J/^oC

dt=temp change = Tfinal-Tinitial

q=(125 J/C)(35.3C-24.5C)

q_soln=+1350 J

|+q_soln|=|-q_rxn|

q_rxn= -1350 J

Find moles magnesium:

moles = mass / molar mass

moles = ?

mass = 0.425 g Mg

molar mass = 24.305 g/mol Mg

moles = 0.425 g / (24.305 g/mol)

=0.017486 moles Mg

Divide, the energy by the moles

-1350 J / 0.017486 moles Mg

= −77200 J / mol Mg

OR

Since 10³ J = 1 kJ

−77.2 kJ / mol Mg