Find the mass of water that vaporizes when 4.04 kg of mercury at 210 °C is added to 0.498 kg of water at 81.6 °C.
I am stuck on trying to figure out how to solve this. Please help!
vaporization takes place while the Hg is above 100C, or 100C+.
so until the water heats to 100, no vaporization.
HeatGained by water+heatgainedHg=0
.498*cwater*(100-81.6)+4.04*CHg*(Tf-210)=0
so calculate Tfinal for the Hg...note it is not in equilibrium with the water temp...
Now, with the water at 100C, and Hg still hot at Tf.
sume of heats gained=0
heatinsteam+heatgainedbyHg=0
Mass*HvWater+.498*Chg*(100-Tfabove)=0
solve for mass...
I'm still not getting the right answer for it...
so, what are your calculations? Maybe we can figure out what's wrong.
To solve this problem, we need to consider the heat transfer between the mercury and water.
The heat transfer equation can be expressed as:
Q = m * c * ΔT
Where:
Q is the heat transfer
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
First, let's calculate the heat transferred from the mercury to the water using the equation above.
For the mercury:
m_mercury = 4.04 kg (given)
c_mercury = 0.139 J/g°C (specific heat capacity of mercury)
ΔT_mercury = 210°C (temperature change of mercury)
Q_mercury = m_mercury * c_mercury * ΔT_mercury
Now let's calculate the heat transferred to the water.
For the water:
m_water = 0.498 kg (given)
c_water = 4.186 J/g°C (specific heat capacity of water)
ΔT_water = 81.6°C (temperature change of water)
Q_water = m_water * c_water * ΔT_water
However, we also need to consider the heat required to vaporize the water. The heat required to vaporize water is given by the equation:
Q_vaporization = m_water * ΔH_vaporization
Where:
ΔH_vaporization is the heat of vaporization of water, which is 2.26 × 10^6 J/kg.
Now let's proceed to calculate the total heat transferred.
Total Q = Q_mercury + Q_water + Q_vaporization
Finally, to find the mass of water that vaporizes, we need to use the equation:
Q_vaporization = m_vaporized * ΔH_vaporization
Rearranging the equation, we can solve for m_vaporized:
m_vaporized = Q_vaporization / ΔH_vaporization
By substituting the values into the equations and simplifying, we can calculate the mass of water that vaporizes.