ChemTopper Free Chemistry Help

Can you explain to me how to do this kind of question type?Screenshot 2026-01-19 133411.png

At thermal equilibrium, the tea and the ice/water mixture are at the same final temperature.

Since the final temperature is 0.0°C, the tea cools from 20.0°C → 0.0°C, so the tea loses heat:

q_tea = m_tea · c · (ΔT)
where ΔT = T_final − T_initial = 0.0 − 20.0 = −20.0°C, so q_tea is negative (heat released).

That same amount of heat is gained by the ice (law of conservation of energy):

q_tea + q_ice = 0
So, q_ice = −q_tea (this will be positive).

Because the ice starts at 0°C and ends at 0°C, the ice does not warm up. The heat it gains is used only for melting (phase change).

Important point: Final temperature being 0°C does NOT mean all the ice melts.
A mixture of ice + liquid water can remain at 0°C at equilibrium. If the tea does not supply enough heat to melt all the ice, some ice will remain.

Decision check (this is the key step)

Calculate heat released by tea
Use density to convert volume to mass:
m_tea = (volume in mL) × (1.00 g/mL)

Then compute:
q_tea = m_tea · c · (−20.0°C)

Compute heat required to melt all the ice
q_{melt all} = m_ice,total · ΔH_fus

Compare

If q_ice < q_{melt all}, then not all ice melts → final remains 0°C, and some solid ice is left.

If q_ice > q_{melt all}, then all ice melts and the leftover heat warms the water above 0°C (you would then use the remaining heat to find T_final).

If some ice remains (q_ice < q_{melt all})

Use:
q_ice = m_melted · ΔH_fus

So:
m_melted = q_ice / ΔH_fus

Then:
m_{ice remaining} = m_ice,total − m_melted