How many grams of methane gas were used to fill a balloon to a volume of \(3.0 \mathrm{~L}\) at STP?

Standard Temperature and Pressure (STP) is a reference point used in chemistry to measure gases. At STP, the temperature is defined as 273.15 K (0°C) and the pressure is 1 atmosphere (atm). This standardization ensures consistency in measurements across different experiments and calculations.

At STP, 1 mole of any ideal gas occupies 22.4 liters. This volume is derived from the Ideal Gas Law under standard conditions. Remembering this value is crucial for solving problems involving gases at STP, like the one we have here.

Knowing the definition and properties of STP helps us perform accurate gas volume and mole calculations. This makes it easier to compare and predict the behavior of gases under these standard conditions.

Moles are a fundamental unit in chemistry that measure the amount of a substance. To solve our problem, we need to convert the given volume of methane gas into moles using the molar volume at STP.

The formula to find the number of moles is:

\( \text{Moles} = \frac{\text{Volume}}{\text{Molar Volume}} \)

For methane at STP, the molar volume is 22.4 liters per mole. Therefore, using the given volume of 3.0 liters:

\( \text{Moles of CH}_4 = \frac{3.0 \text{~L}}{22.4 \text{~L/mol}} = 0.1339 \text{~mol} \)

This calculation tells us how many moles of methane are needed to fill a 3.0-liter balloon at STP.

Calculating the molar mass is essential when converting between moles and grams. The molar mass of a compound is the sum of the atomic masses of all the atoms in its chemical formula.

Methane (CH4) consists of one carbon atom and four hydrogen atoms. Here's how you calculate its molar mass:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.01 g/mol each

So, the molar mass of methane is:

\( \text{Molar Mass of CH}_4 = 12.01 \text{~g/mol (C)} + (4 \times 1.01 \text{~g/mol (H)}) = 16.05 \text{~g/mol} \)

We will use this molar mass to convert the moles of methane into grams.

Methane (CH4) is a simple hydrocarbon and the main component of natural gas. It is one of the most abundant organic compounds found in nature.

Methane consists of one carbon atom bonded to four hydrogen atoms forming a tetrahedral structure. This structure makes methane highly effective as a fuel source because it burns cleanly into carbon dioxide and water with high energy output.

For our problem, methane gas is used to fill a balloon. To find out how many grams of methane are used, we first converted the volume to moles and then used the molar mass:

\( \text{Mass of CH}_4 = \text{Moles of CH}_4 \times \text{Molar Mass of CH}_4 \)

Substituting the values:

\( \text{Mass of CH}_4 = 0.1339 \text{~mol} \times 16.05 \text{~g/mol} = 2.148 \text{~g} \)

Thus, 2.148 grams of methane gas is used to fill the balloon at STP.