determine the mass of ice that will be melting when 1.3g of steam at 102 ° C is passed into a calorimeter containing 80g of ice at 0 ° C
To determine the mass of ice that will melt, we need to calculate the heat transfer that occurs when the steam is passed into the calorimeter with the ice. The heat lost by the steam will be equal to the heat gained by the ice to melt.
First, let's calculate the heat lost by the steam using the formula:
Q = m × c × ΔT
Where:
Q is the heat lost,
m is the mass of the steam,
c is the specific heat capacity of steam, and
ΔT is the change in temperature.
The specific heat capacity of steam is approximately 2.03 J/g°C.
ΔT = (final temperature - initial temperature)
= (0°C - 102°C)
= -102°C
Now, let's calculate the heat lost by the steam:
Q = 1.3g × 2.03 J/g°C × (-102°C)
= -264.78 J
Since energy is conserved, the heat gained by the ice will be equal in magnitude but opposite in sign. So, the heat gain by the ice will be:
Q = -264.78 J
Next, we need to calculate the amount of heat required to melt the ice.
The heat of fusion (ΔH_fusion) of ice is 334 J/g.
Now, let's calculate the mass of ice that will melt:
Q = m × ΔH_fusion
-264.78 J = m × 334 J/g
Divide both sides of the equation by 334 J/g:
m = -264.78 J ÷ 334 J/g
≈ -0.792 g
The negative sign indicates that the ice has lost mass due to melting. However, mass cannot be negative, so we consider only the magnitude of the value:
Mass of ice melted ≈ 0.792 g
Therefore, approximately 0.792 grams of ice will melt when 1.3 grams of steam at 102°C is passed into the calorimeter containing 80 grams of ice at 0°C.