Methane gas, CH4, is sold in a 43.8-L cylinder containing 5.54 kg. What is the pressure inside the cylinder in kilopascals at 20 °C?

Verified step by step guidance

Step 1: Convert the mass of methane (CH4) from kilograms to grams. Since 1 kg = 1000 g, multiply 5.54 kg by 1000 to get the mass in grams.

Step 2: Calculate the number of moles of methane using its molar mass. The molar mass of CH4 is approximately 16.04 g/mol. Use the formula: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass}} \).

Step 3: Convert the temperature from Celsius to Kelvin. Use the formula: \( T(K) = T(°C) + 273.15 \). For 20 °C, calculate the temperature in Kelvin.

Step 4: Use the ideal gas law to find the pressure. The ideal gas law is \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant (8.314 J/mol·K), and \( T \) is the temperature in Kelvin. Rearrange the formula to solve for \( P \): \( P = \frac{nRT}{V} \).

Step 5: Substitute the values for \( n \), \( R \), \( T \), and \( V \) into the equation from Step 4 to calculate the pressure in pascals. Convert the pressure from pascals to kilopascals by dividing by 1000, since 1 kPa = 1000 Pa.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the pressure of a gas when the other variables are known.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For methane (CH4), the molar mass is approximately 16.04 g/mol, calculated from the atomic masses of carbon and hydrogen. Knowing the molar mass is essential for converting the mass of a substance into moles, which is necessary for applying the Ideal Gas Law.

Temperature Conversion

In gas law calculations, temperature must be expressed in Kelvin rather than Celsius. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. For example, 20 °C is equivalent to 293.15 K. This conversion is crucial because the Ideal Gas Law requires absolute temperature for accurate calculations.

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