Question

A backpacker collects snow at 0°C, and places it in a cooking pot on a camp stove. It takes 643 kJ of heat energy to melt the snow and bring the water to boiling. Assuming no heat loss, and neglecting the specific heat capacity of the pot, calculate the mass of snow that the backpacker collected. (The specific heat capacity of liquid water, c = 4.18 J/g.K; and: H₂O(s) -> H₂O(l) /\H = /\Hfusion = 6.02 kJ/mol)A) 1.92 kg B) 1.90 kg C) 1.52 kg D) 855g E) <800g

Answer 1

Answer:

The mass of snow that the backpacker collected is: D) 855g

Explanation:

To boiling the water, the cooking pot requires 643kJ. This heat is due to the heat to melt the water and the heat to bring the water to boiling point.

The heat to melt the water is:

q = ΔHfusion×$\frac{1mol}{18,02g}$×mass

And heat to bring water to boiling point is:

q = C×mass×ΔT

Where C is specific capacity of liquid water and ΔT is change in temperature (100°C, from melting point to boling point)

As the required energy required is 643000J:

643000J =  ΔHfusion×$\frac{1mol}{18,02g}$×mass + C×mass×ΔT

643000J =  6020J/mol×$\frac{1mol}{18,02g}$×mass + 4,18J/g°C×mass×100°C

643000J = 334J/g×mass + 418J/g×mass

643000J = 752J/g×mass

855g = mass

The mass of snow that the backpacker collected is 855g

I hope it helps!

Answer 2

The mass of the snow is 855g

The total heat gained = Latent heat of fusion of ice + heat required to boil water

We have the following information;

H =  643000 J

m =?

L = 6020 J/mol

c = 4.18 J/g.K

Now;

H = mL + mcθ

H = m(L + cθ)

m = H/(L + cθ)

m = 643000 J/[6020 J/mol × 1 mol/18g + (4.18 J/g.K × (100 - 0))]

m = 855g

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