Question

A supplier of cylinder gases warns customers to determine how much gas remains in a cylinder by weighing the cylinder and comparing this mass to the original mass of the full cylinder. In particular, the customer is told not to try to estimate the mass of gas available from the measured gas pressure. Explain the basis of this warning. Are there cases where a measurement of the gas pressure can be used as a measure of the remaining available gas? If so, what are they?

Short answer

The recommendation to weigh the gas cylinder instead of using pressure is due to fluctuating conditions like temperature that can affect the pressure, thereby making it an inaccurate measure. However, in strictly controlled conditions where the temperature and volume don't change, pressure could indeed be used to measure the remaining gas.

Step-by-step solution

Explain the Basis of The Warning

In order to answer the first part of the question we have to refer to the gas laws. According to the ideal gas law \( PV = nRT \), pressure ‘P’ is directly proportional to the number of moles ‘n’ of the gas, provided that the volume ‘V’ and the temperature ‘T’ remains constant. Hence, if the pressure were used as a measure for the amount of gas, it would assume that these conditions hold steadfast - more specifically, that the temperature remains constant. However, in real-life conditions, the temperature can fluctuate which would in turn impact the pressure. Therefore, basing the quantity of gas left on the pressure could lead to an incorrect estimate.

Discuss Cases where Pressure Measurement Could Be Used

As per the ideal gas law, if conditions were such that the temperature and volume remain constant -- meaning no external factors at play which could impact either -- then the gas pressure could indeed be used as a measure of the remaining available gas. Such conditions could exist in a controlled laboratory environment, but are unlikely in everyday applications.

Key concepts

Understanding Gas Laws

The behavior of gases is often described by a series of principles known as gas laws. These laws allow us to understand and predict how a gas will respond to changing conditions such as temperature, volume, and pressure. One foundational law is the ideal gas law, which is expressed by the equation \( PV = nRT \). In this equation, \( P \) represents pressure, \( V \) is the volume, \( n \) indicates the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the absolute temperature.

When we work with an ideal gas, we assume its particles do not attract or repel each other and occupy no space, although no gas actually behaves this way under all conditions. Even so, the ideal gas law serves as a useful approximation for many gases under standard conditions. In the context of the cylinder gas warning, the law reveals why pressure alone isn't a reliable indicator for the amount of gas left — because pressure is linked to both the quantity of gas and the temperature, which can vary outside of controlled environments.

Pressure-Volume Relationships

In gas laws, the relationship between pressure and volume is particularly highlighted by Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is held constant (\(P_1V_1 = P_2V_2\)). However, when considering a real-life situation such as estimating how much gas remains in a cylinder, we cannot overlook temperature's effect on this relationship.

A change in temperature can substantially affect gas pressure. As temperature increases, gas particles move more quickly and collide against the container's walls with greater force, which results in higher pressure. Conversely, lower temperatures will lead to lower pressures. This interdependence makes it challenging to estimate the remaining gas in a cylinder based solely on pressure readings without additional information regarding the temperature.

Chemical Stoichiometry and Gas Measurement

Chemical stoichiometry refers to the calculation of reactants and products in chemical reactions. In the context of gaseous reactions, stoichiometry allows us to relate volumes, pressures, and moles of gases using the ideal gas law. When considering the amount of gas in a cylinder, stoichiometry can be used to determine how many moles of gas \( n \) are present by weighing the cylinder if the molar mass of the contained gas is known.

This approach is more reliable than using pressure measurements, which can vary with temperature, because the mass of the gas does not change with temperature fluctuations. Thus, weighing the cylinder gives a direct assessment of the actual amount of gas available, independent of the gas laws that intertwine pressure, volume, and temperature. This is the basis for the supplier's warning against using pressure to estimate the gas content and exemplifies why an understanding of stoichiometry is essential for accurate measurements in chemistry.