calculate the heat required to change 41.0 g of liquid water at 14.5 C to steam at 100 C and 1 atm. The specific heat of water is 4.184 J/ (g C) and waters enthalpy of vaporization is 2260 J/mol.
q1 = heat needed to raise temperature of liquid H2O from 14.5 C to 100 C,
q1 = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q1 = 41.0 g x 4.184 J/g*C x (100-14.5) = ? J
q2 = heat need to change water @ 100 C to steam @ 100 C
q2 = mass H2O x heat vaporization
q2 = 41.0 g x 1 mol/18.0 g x 2260 J/mol = ?
Qtotal = q1 + q2 = ?
Post your work if you get stuck.
Note: for q2 that 1 mol/18.0 g is to convert the 41.0 g H2O to mols. That is necessary since the heat of vaporization is given in J/mol. It was NOT necessary in q1 since the mass is given in g and the specific heat is given in J/g*C.
To calculate the heat required to change liquid water to steam, you need to consider two steps:
1. Heating the water from its initial temperature (14.5°C) to its boiling point (100°C) at 1 atm.
2. Vaporizing the water at its boiling point.
Let's break down each step:
Step 1: Heating the water
To calculate the heat required to heat the water, we can use the formula: Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Given:
The mass of water (m) = 41.0 g
Specific heat of water (c) = 4.184 J/(g°C)
Change in temperature (ΔT) = (final temperature) - (initial temperature) = (100°C) - (14.5°C)
Q1 = m * c * ΔT
Q1 = (41.0 g) * (4.184 J/(g°C)) * (100°C - 14.5°C)
Step 2: Vaporizing the water
To calculate the heat required to vaporize the water, we can use the formula: Q = n * ΔHvap, where Q is the heat, n is the number of moles, and ΔHvap is the enthalpy of vaporization.
To find the number of moles, we need to use the molar mass of water (18.015 g/mol). The moles (n) can be calculated as follows:
n = (mass)/(molar mass)
n = (41.0 g)/(18.015 g/mol)
Now, let's calculate the heat (Q2) using the given enthalpy of vaporization (ΔHvap).
Q2 = n * ΔHvap
Given:
Enthalpy of vaporization (ΔHvap) = 2260 J/mol
With the values of n and ΔHvap, we can calculate Q2.
Finally, to get the total heat required (Q), we add Q1 and Q2:
Q = Q1 + Q2
Let's substitute the values into the equations and calculate the final answer.