A ten-gallon methane tank contains \(1.243\) mol of methane \(\left(\mathrm{CH}_{4}\right)\) at \(74^{\circ} \mathrm{F}\). Express the volume of the tank in liters, the amount of methane in the tank in grams, and the temperature of the tank in Kelvin.

Short Answer

Expert verified
Answer: The volume of the tank is 37.8541 liters, the amount of methane in the tank is 19.955 grams, and the temperature of the tank is 296.4833 Kelvins.

Step by step solution

01

Convert the volume of the tank from gallons to liters

To convert the volume from gallons to liters, we can use the conversion factor: 1 gallon = 3.78541 liters. So, we have: $$ \text{Volume in liters} = \text{Volume in gallons} \times \text{Conversion factor} $$ $$ \text{Volume in liters} = 10 \times 3.78541 = 37.8541 \text{ L} $$
02

Convert the amount of methane from moles to grams

To convert the amount of methane from moles to grams, we need to multiply the given moles by the molar mass of methane: $$ \text{Mass in grams} = \text{Moles} \times \text{Molecular weight} $$ Molecular weight of methane (\(\mathrm{CH}_{4}\)) = \(12.01 (\mathrm{C}) + 4 \times 1.008(\mathrm{H}) = 16.042 \text{ g/mol}\) $$ \text{Mass in grams} = 1.243 \text{ mol} \times 16.042 \frac{\text{g}}{\text{mol}} = 19.955 \text{ g} $$
03

Convert the temperature from Fahrenheit to Kelvin

To convert the temperature from Fahrenheit to Kelvin, we need to use the following conversions: 1. Convert Fahrenheit to Celsius: \((°\mathrm{F} - 32) \times \frac{5}{9} = °\mathrm{C}\) 2. Convert Celsius to Kelvin: \(°\mathrm{C} + 273.15 = \mathrm{K}\) First, convert the given temperature from Fahrenheit to Celsius: $$ \text{Temperature in Celsius} = (74 - 32) \times \frac{5}{9} = 23.3333 °\mathrm{C} $$ Next, convert the temperature from Celsius to Kelvin: $$ \text{Temperature in Kelvin} = 23.3333 + 273.15 = 296.4833\mathrm{K} $$ Therefore, the volume of the tank is \(37.8541 \text{ L}\), the amount of methane in the tank is \(19.955 \text{ g}\), and the temperature of the tank is \(296.4833 \mathrm{K}\).

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