Question

In: Chemistry

7.1 g of water ice at 268.4 K is mixed with 234 g of liquid water...

7.1 g of water ice at 268.4 K is mixed with 234 g of liquid water at 304.7 K in an insulated container under an external pressure of 1.00 bar. Answer the following questions assuming that the physical properties of water and ice are constant over the range of interest. Physical properties for water and ice are given below:

Cp,m,ice = 1.95 J g-1 K-1
ΔHfusion,ice = 333.4 J g-1
Cp,m,water = 4.18 J g-1 K-1
Melting point of ice: 273.15 K

1) What will be the final form of the system? Select one that applies

(a)
Water

(b)
Mixed water and ice

Solutions

Expert Solution

1. a) water

2. 301.3 K

Explanation:

The calculation is done assuming that the final temperature would be such that it will melt the 7.1 g of water ice at 268.4 K and increase the temperature of the resulting water as the 234 g of liquid water at 304.7 K is mixed to the water ice. This assumption is valid as can be seen from the value of final temperature.

Final temperature when the system reaches equilibrium = T_f K

Mass of ice = 7.1 g

Temperature of ice (T_ice) = 268.4 K

Specific heat of ice, (C_p,m) = 1.95 J g^-1 K^-1

Heat absorbed by ice to reach 273.15 K = mass of ice x specific heat of ice x (273.15- T_ice)

= 7.1 g x 1.95 J g^-1 K^-1 x(273.15 - 268.4) K

= 65.76 J

Heat absorbed on melting of ice = mass of ice x ΔH_fusion,ice

= 7.1 g x 333.4 J g^-1

= 2367 J

Heat absorbed by the melted ice (i.e. water) = mass of melted ice (i.e. water) x specific heat of water x (T_f- 273.15 K)

= 7.1 g x 4.18 J g^-1 K^-1 x (T_f- 273.15) K

= 29.68 x (T_f- 273.15) J

Mass of water mixed = 234 g

Temperature of water (T_water) = 304.7 K

Specific heat of water, (C_p,m) = 4.18 J g^-1 K^-1

Heat released by water = mass of water x specific heat of water x (T_f - T_water)

= 234 g x 4.18 J g^-1 K^-1 x (T_f - 304.7) K

= 978.1 x (T_f - 304.7) J

Now,

total heat absorbed + total heat released = 0

or, 65.76 J + 2367 J + 29.68 x (T_f- 273.15) J + 978.1 x (T_f - 304.7) J = 0

or, 2433 J + 29.68T_f J - 8107 J + 978.1T_f J - 298027 J = 0

or, 1008T_f = 303701

or, T_f = 301.3 K

Thus, the final temperature (T_f) of the system when it reaches equilibrium = 301.3 K

At this temperature of 301.3 K, the final form of the system is (a) Water.

queen_honey_blossom answered 10 months ago

Next > < Previous

Related Solutions

A 50.0-g sample of liquid water at 25.0°C is mixed with 35.0 g of water at...

A 50.0-g sample of liquid water at 25.0°C is mixed with 35.0 g of water at 89.0°C. The final temperature of the water is ________°C.

100 g of ice at -20°C are mixed with 250 g of water at 20°C in...

100 g of ice at -20°C are mixed with 250 g of water at 20°C in an insulated calorimeter. What is the final temperature of the system? How many grams of liquid water and how many grams of ice will you find after the system equilibrates? find T in degrees C; m of solid (in grams); m of liquid (in grams) T=____ ms=____ mliq=____

100 g of solid ice at 0°C is added to 500 g of liquid water at...

100 g of solid ice at 0°C is added to 500 g of liquid water at 90°C. What is the final temperature? What is initial water temperature is required so that 10 g of ice remain once equilibrium has been reached?

190 g of ice at 0 ºC is mixed with 49 g of steam at 100...

190 g of ice at 0 ºC is mixed with 49 g of steam at 100 ºC to make water. The latent heat of fusion of water is 33.5 × 104 J/kg, and the specific heat of water is 4186 J/kg∙K, the latent heat of vaporization of water is 22.6 × 105 J/kg. A) Determine the amount of heat released by steam at 100*C to make water at 100*C. B) Determine the amount of heat absorbed by ice at 0*C...

Estimatethe total entropy change when 100.g of liquid water, initially at 298 K and 0.50 atm,is...

Estimatethe total entropy change when 100.g of liquid water, initially at 298 K and 0.50 atm,is first heated to boiling at 373 K and 1.00atm, and the steamcollected at 1.00 atmsubsequently heated and compressed to 500Kand20.atm. UseDHvap(at 100 ̊C, 1 atm)= 40.6 kJ/mol and the following values for the heat capacity:CP,m(H2O,l) = 75.2 J/(K mol), CP,m(H2O,g) = 35.0J/(K mol)

Water changes between solid phase (as ice) and liquid phase at 0℃. and between liquid phase and gas phase (as water vapor) at 100 ℃.

Water changes between solid phase (as ice) and liquid phase at 0℃. and between liquid phase and gas phase (as water vapor) at 100 ℃. Write a program to accept a temperature front keyboard, and display the corresponding water phase (solid, liquid or gas) under that temperature.

1200 g of antifreeze, C2H6O2, is mixed with 1000 g of water, H2O. What is the...

1200 g of antifreeze, C2H6O2, is mixed with 1000 g of water, H2O. What is the boiling point of the solution? Kb.p= 0.51 degrees C/m for water

The standard molar entropies of water ice, liquid, and vapor are $37.99, 69.91$, and $188.83 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$,

The standard molar entropies of water ice, liquid, and vapor are $37.99, 69.91$, and $188.83 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, respectively. On a single graph, show how the Gibbs energies of each of these phases vary with temperature.

Ice floats on water. For most other substances however, the solid sinks in the liquid.

Ice floats on water. For most other substances however, the solid sinks in the liquid. Classify each of these statements as true for water, or true for most other substances.

a. 0.130 g of HCl is in 35.0 mL of water. This is mixed with 50.0...

a. 0.130 g of HCl is in 35.0 mL of water. This is mixed with 50.0 mL of 0.185 M Sr(OH)2. What is the pH of the resulting solution? b. Calculate the pH of a solution prepared by mixing 125.0 mL of 0.0120 M HCl with 25.0 mL of 0.0420 M Ba(OH)2? c.

Subjects