What mass (in grams) of CaCl2(s) must be dissolved in pure water at 10.0 deg Celsius to make a 26.4 mL solution and to increase the solution temperature to 16.4 deg Celsius? Assume that there is no heat loss from the solution and that the solution has the same physical properties as pure water.

Question

What mass (in grams) of CaCl2(s) must be dissolved in pure water at 10.0 deg Celsius to make a 26.4 mL solution and to increase the solution temperature to 16.4 deg Celsius? Assume that there is no heat loss from the solution and that the solution has the same physical properties as pure water.

Data:
DHsol(CaCl2)(s)) = - 82.8 kJ.mol-1

specific heat of water = 4.184 J.g-1.deg-1

density of water = 1.00 g.cm-3

molar mass of CaCl2 = 111 g/mol

Answer 1

(26.4mL)(1.00g/mL) = 26.4g H2O

To raise the temperature of 26.4 g H2O by (16.4 C- 10.0 C), we need:
(4.18 J/g.C)(26.4 g)(6.4 C) = 706 J needed

- 82.8 kJ.mol-1 CaCl2 is equivalent to:
82800 J / 111g CaCl2 = 746 J/g CaCl2 released.

Use the values: 706 J needed and 746 J/g CaCl2 released to get the grams of CaCl2 that must be used.

Answer 2

thank u sooooooooooo much :)

Answer 3

To solve this problem, we need to calculate the energy required to heat the solution from 10.0°C to 16.4°C and then use that information to find the mass of CaCl2(s) that must be dissolved.

First, let's calculate the energy required to heat the solution:

1. Calculate the change in temperature:
ΔT = T_final - T_initial = 16.4°C - 10.0°C = 6.4°C

2. Convert the change in temperature to Kelvin:
ΔT_K = ΔT + 273.15 = 6.4°C + 273.15 = 279.55 K

3. Calculate the energy required to heat the solution using the specific heat formula:
q = m * c * ΔT_K

Where:
q = heat energy (Joules)
m = mass of the solution (in grams) - which is what we need to find
c = specific heat capacity of water (4.184 J/g°C)
ΔT_K = change in temperature in Kelvin

Now, let's calculate the mass of the solution:

1. Rearranging the equation, we have:
m = q / (c * ΔT_K)

2. Plug in the values:
m = q / (4.184 J/g°C * 279.55 K)

Note: We need to convert the specific heat from J/g°C to kJ/g°C since the DHsol value is given in kJ/mol.

m = q / (4.184 kJ/g°C * 279.55 K)

3. Calculate the energy required to heat the solution:
q = DHsol * n

Where:
DHsol = enthalpy of solution (-82.8 kJ/mol)
n = number of moles of CaCl2 (which we need to find)

To find the number of moles, we will use the formula:
n = m / M

Where:
M = molar mass of CaCl2 (111 g/mol)

4. Substituting the expression for q in terms of n:
m = (DHsol * n) / (4.184 kJ/g°C * 279.55 K * M)

Plugging in the values for DHsol, M, and the calculations for q:

m = (-82.8 kJ/mol * n) / (4.184 kJ/g°C * 279.55 K * 111 g/mol)

Now, we can solve for the mass.

Note: It's important to consider the units while performing the calculations and convert as necessary to ensure compatibility.