Question

An electric power station annually burns \(3.1 \times 10^{7} \mathrm{~kg}\) of coal containing 2.4 percent sulfur by mass. Calculate the volume of \(\mathrm{SO}_{2}\) emitted at STP.

Short answer

The volume of \(\mathrm{SO}_2\) emitted is approximately \(5.20 \times 10^8 \ \text{L}\) at STP.

Step-by-step solution

Calculate the Mass of Sulfur

First, find out how much sulfur is in the coal. Since the coal contains 2.4% sulfur by mass, you can calculate the mass of sulfur by multiplying the total mass of coal by 2.4%.\[ \text{Mass of Sulfur} = (3.1 \times 10^7 \ \text{kg}) \times 0.024 = 7.44 \times 10^5 \ \text{kg} \]

Convert Mass of Sulfur to Moles

We need to know how many moles of sulfur are in the coal because 1 mole of sulfur will form 1 mole of \(\mathrm{SO}_2\). Use the molar mass of sulfur (approximately 32.07 g/mol) to convert the mass to moles. Remember to convert kilograms to grams (1 kg = 1000 g).\[ \text{Moles of Sulfur} = \frac{7.44 \times 10^5 \ \text{kg} \times 1000 \ \text{g/kg}}{32.07 \ \text{g/mol}} \approx 2.32 \times 10^7 \ \text{mol} \]

Calculate Moles of SO2

Each mole of sulfur produces a mole of \(\mathrm{SO}_2\). So, the number of moles of \(\mathrm{SO}_2\) will equal the number of moles of sulfur.\[ \text{Moles of } \mathrm{SO}_2 = 2.32 \times 10^7 \ \text{mol} \]

Calculate Volume of SO2 at STP

At Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 liters. Multiply the moles of \(\mathrm{SO}_2\) by 22.4 L/mol to find the volume of \(\mathrm{SO}_2\).\[ \text{Volume of } \mathrm{SO}_2 = 2.32 \times 10^7 \ \text{mol} \times 22.4 \ \text{L/mol} \approx 5.20 \times 10^{8} \ \text{L} \]

Key concepts

Sulfur Dioxide Calculation

Sulfur dioxide (\( \mathrm{SO}_2 \)) is a common byproduct when burning coal containing sulfur. When calculating the amount of \( \mathrm{SO}_2 \) emitted, it's essential to understand the transformation from sulfur present in the coal to the gaseous \( \mathrm{SO}_2 \). Initially, determine the mass percentage of sulfur in the coal. In our example, the coal contains 2.4% sulfur. This means for every kilogram of coal burned, 24 grams is sulfur. Knowing this allows you to compute the total mass of sulfur combusted over a specified period or quantity of coal.Next, use the relationship between sulfur and sulfur dioxide: every mole of sulfur results in a mole of \( \mathrm{SO}_2 \) because the \( \mathrm{SO}_2 \) molecule consists of one sulfur and two oxygen atoms. In practice, understanding this stoichiometric relation is crucial in predicting the amount of sulfur dioxide produced from a given amount of sulfur.

Molar Mass Conversion

Molar mass conversion is a fundamental concept in chemistry that helps convert between the mass of a substance and the number of moles. For sulfur, whose atomic mass is approximately 32.07 g/mol, this conversion is straightforward: divide the mass of sulfur by its molar mass to find the number of moles. Remember to be consistent with units, so convert kilograms to grams by multiplying by 1000. This approach is applicable for any element or compound. For example, knowing the molar mass of a compound allows chemists to convert grams into moles, which is essential for stoichiometric calculations. It serves as a bridge between the macroscopic world (mass in grams or kilograms) and the microscopic world (amount in moles), leading to more accurate chemical predictions and industrial applications.

Standard Temperature and Pressure

Standard Temperature and Pressure (STP) is a set of conditions commonly used in chemistry to simplify calculations. STP is defined as a temperature of 0 degrees Celsius (273.15 Kelvin) and a pressure of 1 atmosphere (101.3 kPa). At STP, one mole of any ideal gas occupies 22.4 liters.Understanding STP is significant when calculating gas volumes in chemical reactions. The consistent conditions allow for direct comparisons and conversions between moles of gas and volume. In the context of sulfur dioxide emissions, once the moles of \( \mathrm{SO}_2 \) are known, you can easily calculate volume. Simply multiply the moles by 22.4 L/mol to find the total volume of gas produced at STP.This standardization simplifies the often complex task of predicting gas behavior in different environmental settings, making it a critical concept in both academic and industrial application of chemistry.