A ten gallon methane tank contains 1.243 mol of methane at 74°F. Express the volume of tank in liters, the amount of methane in the tank in grams, and the tempature of the tank in kelvin.
First, convert 74F to celsius. Convert 10 gallon to liters. Use google to do this if you don't have the conversion factor.
grams = mols x molar mass
Kelvin = 273 + C
296
To convert the volume of the tank from gallons to liters, you can use the conversion factor that 1 gallon is equal to approximately 3.785 liters.
Volume of tank in liters = 10 gallons * 3.785 liters/gallon
Volume of tank in liters = 37.85 liters
To convert the amount of methane in the tank from moles to grams, you need to use the molar mass of methane, which is approximately 16.04 grams/mol.
Amount of methane in grams = 1.243 mol * 16.04 grams/mol
Amount of methane in grams = 19.92 grams
To convert the temperature of the tank from Fahrenheit (°F) to Kelvin (K), you can use the equation:
Kelvin (K) = 5/9 * (Fahrenheit (°F) - 32) + 273.15
Temperature of the tank in Kelvin = (5/9 * (74°F - 32)) + 273.15
Temperature of the tank in Kelvin = (5/9 * 42°F) + 273.15
Temperature of the tank in Kelvin = (5/9 * 5/9 * 42°C) + 273.15
Temperature of the tank in Kelvin = (5/9 * 5/9 * (42 + 273.15)) + 273.15
Temperature of the tank in Kelvin ≈ 298.706 K (rounded to the nearest thousandth)
Therefore, the volume of the tank is approximately 37.85 liters, the amount of methane in the tank is approximately 19.92 grams, and the temperature of the tank is approximately 298.706 Kelvin.
To solve this problem, we need to convert between different units. Let's break it down step by step:
1. Convert the volume of the tank from gallons to liters:
- 1 gallon = 3.78541 liters
- So, 10 gallons * 3.78541 liters/gallon = 37.8541 liters
The volume of the tank is 37.8541 liters.
2. Convert the amount of methane from moles to grams:
- The molar mass of methane (CH4) is 16.04 g/mol (carbon: 12.01 g/mol, hydrogen: 1.01 g/mol)
- Multiply the number of moles (1.243 mol) by the molar mass (16.04 g/mol):
1.243 mol * 16.04 g/mol = 19.94 grams
The amount of methane in the tank is 19.94 grams.
3. Convert the temperature from Fahrenheit to Kelvin:
- The conversion formula is: K = (°F + 459.67) * 5/9
- Plug in the temperature in Fahrenheit (74°F):
K = (74 + 459.67) * 5/9
K = 297.04 * 5/9
K = 164.47 Kelvin (rounded to two decimal places)
The temperature of the tank is 164.47 Kelvin.