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When working with gases, pressure calculations are often crucial. Using the Ideal Gas Law, we can determine the pressure within a container. This is especially true when you know the amount of gas, the volume of the tank, and the temperature. The Ideal Gas Law is expressed as:

\[ P = \frac{nRT}{V} \]
Here:

• \( P \) is the pressure,
• \( n \) represents the number of moles of the gas,
• \( R \) is the universal gas constant with a value of 8.314 J/(mol·K),
• \( T \) is the temperature in Kelvin,
• and \( V \) is the volume in cubic meters.

It's important to always double-check your unit conversions!
For our helium tank problem, applying the given values to the formula produces a pressure of approximately 141,970 Pa. Converting this to atmospheres is simple by remembering that 1 atmosphere equals 101,325 Pa. This means approximately 1.4 atm, showing just how pressure increases with a relatively small amount of helium.

Understanding moles is a vital part of chemistry, especially when working with gases. The mole is a unit that measures the amount of substance. In our helium example, calculating the number of moles starts with converting the mass from kilograms to grams because the molar mass is given in grams/mole.

Since the mass of helium is given as \(4.86 \times 10^{-4}\) kg, which equals 0.486 g, we can then use the mole formula:

\[ n = \frac{m}{M_m} \]
Where \( n \) is the number of moles, \( m \) is the mass in grams, and \( M_m \) is the molar mass, 4.00 g/mol for helium.

Thus, \( n \) equals \( \frac{0.486}{4.00} \), amounting to about 0.1215 moles. Recognizing this small quantity of helium is crucial for calculating how it contributes to the overall gas pressure inside the tank.

Temperature is a critical factor in the behavior of gases. In the Ideal Gas Law, we must not forget that temperature should always be represented in Kelvin. This involves converting from commonly used Celsius.

Temperature conversion from Celsius to Kelvin is straightforward:

• Add 273.15 to the Celsius temperature to get the Kelvin figure.

For helium at 18.0°C, the conversion is:

\[ T = 18.0 + 273.15 = 291.15~K \]
This conversion is vital because the Kelvin scale is an absolute temperature scale starting from absolute zero, where theoretically, all particle motion ceases. Using Kelvin ensures that the calculations in the Ideal Gas Law remain consistent and accurate. Take note that using Celsius directly without converting to Kelvin would lead to incorrect results.