. Mountain climbers often brew tea by melting snow, which they heats over a stove. Our stove
burns butane (C4H10), which has a heat of combustion of -2878 kJ/mol. The temperature of the
snow is initially at -20 °C, and we need 80 °C water to brew tea.
a. How much heat is needed to turn the snow into a cup (237 mL) of water hot enough to
make a cup of tea?
b. Calculate the mass of butane needed to fuel the stove for this process
For part A i calculated Q to be 99.1608 kJ/mol. I don't understand where to go from there though to find part b.
To solve this problem, we need to consider the heat required to melt the snow and heat the water, as well as the amount of butane needed to produce that heat.
a. Firstly, let's calculate the heat required to turn the snow into water at 0°C (melting point). The heat required to melt one mole of ice is 6.01 kJ/mol.
The molar mass of water (H2O) is 18.01 g/mol, and the density of water is approximately 1 g/mL.
Since we want to melt a cup (237 mL) of snow, the number of moles of ice can be calculated as follows:
Moles of ice = (237 mL / 1000 mL) x 1 g/mL / 18.01 g/mol
Next, we can calculate the heat required to melt the snow:
Heat for melting snow = Moles of ice x Heat of fusion of ice
Heat for melting snow = Moles of ice x 6.01 kJ/mol
b. To calculate the mass of butane needed, we need to use the enthalpy of combustion of butane and the heat required to heat the water.
The heat required to raise the temperature of the water can be calculated using the formula:
q = m x C x ∆T
Where:
q = heat required
m = mass of water
C = specific heat capacity of water (assuming 4.18 J/g°C)
∆T = change in temperature (80°C - 0°C)
Now, we can calculate the mass of water needed to make a cup of tea:
Mass of water = 237 mL x 1 g/mL = 237 g
Finally, we can calculate the heat required to heat the water:
Heat for heating water = Mass of water x C x ∆T
Heat for heating water = Mass of water x 4.18 J/g°C x 80°C
Since we know the heat of combustion of butane (-2878 kJ/mol), we can determine the amount of butane needed to produce the required heat.
Mass of butane = (Heat for melting snow + Heat for heating water) / Heat of combustion of butane
Please note that the specific heat capacity of water and the heat of fusion of ice may vary slightly depending on experimental conditions.
To calculate the heat needed to turn the snow into hot water, we can follow these steps:
a. Calculate the heat needed to raise the temperature of the snow from -20 °C to 0 °C.
b. Calculate the heat needed to melt the snow at 0 °C.
c. Calculate the heat needed to raise the temperature of the water from 0 °C to 80 °C.
d. Sum up the heat from all three steps to get the total heat required.
Let's go through each step:
Step a: Calculate the heat needed to raise the temperature of the snow from -20 °C to 0 °C.
We will use the specific heat capacity of snow, which is approximately 2.09 J/g·°C. The specific heat capacity represents the amount of heat required to raise the temperature of 1 gram of a substance by 1 °C.
To convert from °C to Kelvin, we add 273.15.
The temperature difference is 0 °C - (-20 °C) = 20 °C.
The mass of the snow is not given, so let's assume it as 237 mL, which is equivalent to 237 grams (as the density of water is 1 g/mL).
The heat required to raise the temperature of the snow is:
Heat = mass × specific heat capacity × temperature difference
Heat = 237 g × 2.09 J/g·°C × 20 °C
Heat = 9915.66 J
Step b: Calculate the heat needed to melt the snow at 0 °C.
The heat of fusion is the amount of heat required to convert 1 gram of a substance from solid to liquid without changing its temperature. For ice, it is approximately 334 J/g.
The mass of the snow is again 237 g.
The heat required to melt the snow is:
Heat = mass × heat of fusion
Heat = 237 g × 334 J/g
Heat = 79158 J
Step c: Calculate the heat needed to raise the temperature of the water from 0 °C to 80 °C.
Now, we'll use the specific heat capacity of water, which is approximately 4.18 J/g·°C.
The temperature difference is 80 °C - 0 °C = 80 °C.
The mass of the water is given as 237 g.
The heat required to raise the temperature of the water is:
Heat = mass × specific heat capacity × temperature difference
Heat = 237 g × 4.18 J/g·°C × 80 °C
Heat = 79716.24 J
Step d: Sum up the heat from all three steps to get the total heat required.
Total Heat = Heat from Step a + Heat from Step b + Heat from Step c
Total Heat = 9915.66 J + 79158 J + 79716.24 J
Total Heat = 168789.9 J
So, the total heat required to turn the snow into a cup (237 mL) of water hot enough to make a cup of tea is approximately 168789.9 J.
Now, let's move on to calculating the mass of butane needed to fuel the stove for this process.
b. Calculate the mass of butane needed to fuel the stove for this process.
We know the heat of combustion of butane is -2878 kJ/mol. To calculate the mass of butane needed, we need to convert the heat requirement to joules.
1 kJ = 1000 J.
Heat required = Total Heat (from above) in joules = 168789.9 J.
Heat required in kJ = Heat required / 1000 = 168789.9 J / 1000 = 168.79 kJ.
Now, we can use the heat of combustion to calculate the amount of butane needed.
Heat of combustion of butane = -2878 kJ/mol.
Let's assume the molar mass of butane (C4H10) is 58.12 g/mol.
The mass of butane needed can be calculated using the following formula:
Mass of butane = Heat required (in kJ) / Heat of combustion (in kJ/mol) × Molar mass of butane (in g/mol)
Mass of butane = 168.79 kJ / 2878 kJ/mol × 58.12 g/mol
Mass of butane = 1.908 g
Therefore, approximately 1.908 grams of butane would be needed to fuel the stove for this process.