Askiitians Tutor Team
Last Activity: 5 Months ago
To determine how much water can be produced from burning ethylene, we first need to calculate the energy released from the combustion of the ethylene and then see how much ice can be melted with that energy. Let's break this down step by step.
Understanding Ethylene Combustion
Ethylene (C2H4) combusts in the presence of oxygen to produce carbon dioxide and water. The combustion reaction can be summarized as follows:
C2H4 + 3 O2 → 2 CO2 + 2 H2O
From the problem, we know that burning one mole of ethylene releases 340 kcal of energy. First, we need to find out how many moles of ethylene are in the 4.2 g cylinder.
Calculating Moles of Ethylene
The molar mass of ethylene (C2H4) is calculated as follows:
- Carbon (C): 12.01 g/mol × 2 = 24.02 g/mol
- Hydrogen (H): 1.008 g/mol × 4 = 4.032 g/mol
- Total molar mass = 24.02 g/mol + 4.032 g/mol = 28.052 g/mol
Now, we can calculate the number of moles of ethylene in 4.2 g:
Number of moles = mass (g) / molar mass (g/mol)
Number of moles = 4.2 g / 28.052 g/mol ≈ 0.149 moles
Energy Released from Combustion
Next, we calculate the total energy released from burning 0.149 moles of ethylene:
Total energy = moles × energy per mole
Total energy = 0.149 moles × 340 kcal/mole ≈ 50.6 kcal
Melting Ice with the Released Energy
To melt ice, we need to know how much energy is required to convert ice at 0°C to water at 0°C. The latent heat of fusion for ice is approximately 80 kcal/kg. Therefore, to melt 1 kg of ice, we need:
Energy required = mass × latent heat of fusion
Energy required = 1 kg × 80 kcal/kg = 80 kcal
Comparing Energy Values
Now, we compare the energy released from the combustion of ethylene (50.6 kcal) with the energy required to melt 1 kg of ice (80 kcal). Since 50.6 kcal is less than 80 kcal, we cannot melt the entire 1 kg of ice. Instead, we can determine how much ice can be melted with the available energy.
To find out how much ice can be melted with 50.6 kcal:
Mass of ice melted = energy available / latent heat of fusion
Mass of ice melted = 50.6 kcal / 80 kcal/kg ≈ 0.6325 kg
Converting Mass of Water to Volume
Since the density of water is approximately 1 g/ml, we can convert the mass of water melted into volume:
Volume of water (ml) = mass of water (g)
Given that 0.6325 kg of ice melts into 0.6325 kg of water, we convert this to grams:
0.6325 kg = 632.5 g
Thus, the volume of water available for drinking is:
Volume = 632.5 ml
Final Result
In summary, by burning the ethylene, the person can produce approximately 632.5 ml of water from melting ice. This calculation highlights the importance of energy conversion and the practical applications of chemistry in survival situations.
