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In combustion reactions, theoretical air is the exact amount of air required for complete combustion of a given fuel. It's based on the stoichiometry of the reaction, meaning the exact ratio of fuel to oxygen needed to ensure all the fuel combusts completely without any leftover. For butane \(\text{C}_{4} \text{H}_{10}\), the reaction with theoretical air can be defined as: \[ \text{C}_{4} \text{H}_{10} + 6.5(\text{O}_{2} + 3.76 \text{N}_{2}) \rightarrow 4 \text{CO}_{2} + 5 \text{H}_{2}\text{O} + 24.44 \text{N}_{2} \] However, in the problem at hand, the air supplied is 150% of theoretical air. To account for this, you'll need to multiply the moles of oxygen and nitrogen by 1.5. The adjusted equation is: \[ \text{C}_{4} \text{H}_{10} + 9.75(\text{O}_{2} + 3.76 \text{N}_{2}) \rightarrow 4 \text{CO}_{2} + 5 \text{H}_{2}\text{O} + 36.66 \text{N}_{2} \] By increasing the air supplied, you ensure complete combustion.

Relative humidity is the amount of water vapor present in the air, expressed as a percentage of the amount needed for saturation at the same temperature. In other words, it's how 'full' the air is with water vapor. The problem specifies 80% relative humidity at 30°C. At this temperature, using tables, the saturation pressure of water vapor is about 31.8 mmHg. Therefore, the partial pressure of water vapor is calculated as: \[ P_{water} = 0.8 \times 31.8 \text{mmHg} = 25.44 \text{mmHg} \] Considering this partial pressure is crucial for calculating the dew point temperature later.

The dew point temperature is the temperature at which air becomes saturated with water vapor and condenses into liquid. To find the dew point of the products from the combustion, we need to know the partial pressure of water vapor in the gases. Given an 80% relative humidity air, the partial pressure of water vapor is 25.44 mmHg. So, the dew point is the temperature at which the water vapor has this partial pressure. Using tables that relate temperature to saturation pressure, you can find the corresponding dew point. Generally, the closer the air is to saturation, the higher the dew point.

Balancing a chemical equation ensures the number of moles of each element is the same on both sides of the equation. For butane combustion: \[ \text{C}_{4} \text{H}_{10} + 6.5 (\text{O}_{2} + 3.76 \text{N}_{2}) \rightarrow 4 \text{CO}_{2} + 5 \text{H}_{2}\text{O} + 24.44 \text{N}_{2} \] Here, the carbon atoms (4) balance with 4 \(\text{CO}_{2}\) molecules, and hydrogen atoms (10) balance with 5 \(\text{H}_{2}\text{O}\) molecules. Nitrogen remains unaffected and appears in the same amount on both sides. This balance ensures mass conservation and proper reaction representation.

The ideal gas law is an equation of state for an ideal gas, expressed as \[ PV = nRT \] Where \P\ is pressure, \V\ is volume, \ is the number of moles, \R\ is the gas constant, and \T\ is temperature in Kelvin. This law is useful for understanding the behavior of gases, especially when calculating the partial pressure of water vapor in the air and its contribution to the total pressure. Using this equation can help convert volumes and pressures of gases to standard conditions, facilitating various calculations, like those needed for determining the dew point.