# Boiling Point of Water: Examples and Calculations

## The Boiling Point of Water

The **boiling point** refers to the temperature at which a liquid begins to bubble and convert to a gas. Calculations are commonly performed for the boiling point of water. The boiling point of water is very important in many scenarios, such as for food processing and making canned foods, or using steam as a power source.

The boiling point of a liquid can change based on several factors, including altitude, air pressure, or the presence of other constituents in the liquid (such as salt or sugar). When heating up water the temperature of the water continues to rise, but remains a liquid until it reaches a critical point. At this boiling point, a few things begin to happen:

- The liquid converts to gas
- Temperature of the liquid no longer increases
- Vapor pressure of the liquid is equal to surrounding air pressure

At a liquid's boiling point bubbles will form on the surface of the water, because the water now has enough energy from the heat to break the surface tension of the water, thus forming bubbles. When water reaches this critical point it does not increase in temperature any further. Instead any additional energy (heat) added to the water changes the state of the water from a liquid to a gas, creating steam. This critical point is achieved when the vapor pressure of the water is equal to the air pressure surrounding the water, which is why the boiling point changes at different air pressures. This also explains why the boiling point changes with altitude, because different altitudes have different air pressures.

### What is the Boiling Point of Water at Sea Level?

The boiling point of water is often calculated at sea level, which correlates to zero feet or meters in elevation. The boiling point of water at sea level is 100 degrees Celsius, or 212 degrees Fahrenheit. However, as mentioned earlier, the boiling point of water changes with altitude. This means that water will boil at different temperatures in locations that are at different altitudes.

City | Elevation | Boiling Point of Water in Degrees Celsius |
---|---|---|

Washington D.C. | 0 m | 100 |

Calgary, Canada | 1045 m | 96.6 |

Bogota, Columbia | 2619 m | 91.3 |

Lhasa, China | 3490 m | 88.2 |

La Rinconada, Peru | 5100 m | 82.5 |

As seen in this chart, as the elevation of the city increases, the boiling point of water decreases. As altitude increases, the air pressure decreases. As the air pressure decreases, less energy (heat) is required in order to increase the vapor pressure of the water so that it equals the surrounding air pressure. As a result, the boiling point decreases as elevation increases.

### Water Boiling Point Pressure Chart

The reason that boiling point decreases as elevation increases is because the air pressure decreases as elevation increases. A lower air pressure means a lower boiling point, and a higher air pressure means a higher boiling point. This graph shows how the boiling point changes as the pressure changes:

As shown in this graph, the boiling point temperature of a liquid increases as the air pressure increases. Also notice that the relationship isn't strictly linear (a straight line). Instead it curves, such that the increase in boiling point initially changes rapidly with any change in air pressure. However, as the air pressure gets higher and higher, the change in boiling point temperature doesn't change as quickly. This means the relationship between boiling point and air pressure is a logarithmic function, which is demonstrated by the equation used to find the boiling point of water from the pressure.

## Boiling Point Calculations for Water

As mentioned, the boiling point of water at sea level standard pressure is 100 degrees Celsius, or 212 degrees Fahrenheit. Standard pressure refers to the air pressure that is standard at sea level. The value for standard pressure is:

- 14.7 atm
- 760 mm Hg
- 101325 Pa

However, it is important to know how to calculate the boiling point of a liquid at different pressures and altitudes as well.

### How to Calculate Boiling Point of Water at Different Pressures

The following formula can be used in order to calculate the boiling point of water at different pressures:

{eq}ln \frac{pressure}{101325} = 4890(\frac{1}{373} - \frac{1}{boiling point}) {/eq}.

In this formula, pressure is in pascals (Pa) and temperature is in Kelvin (K). Let's start with finding the boiling point of water if the air pressure is 245,675 Pa. We substitute the known air pressure value into the formula:

{eq}ln \frac{245675}{101325} = 4890(\frac{1}{373} - \frac{1}{boiling point}) {/eq}

And solve for boiling point:

- Simplify fraction: {eq}ln (2.42) = 4890(\frac{1}{373} - \frac{1}{boiling point}) {/eq}

- Take the natural log: {eq}0.886 = 4890(\frac{1}{373} - \frac{1}{boiling point}) {/eq}

- Divide both sides by 4890: {eq}1.811 \times 10^-4 = \frac{1}{373} - \frac{1}{boiling point} {/eq}

- Isolate boiling point fraction: {eq}\frac{1}{boiling point} = \frac{1}{373} - 1.811 \times 10^-4 {/eq}

- Solve subtraction: {eq}\frac{1}{boiling point} = 0.0025 {/eq}

- Isolate boiling point: {eq}\frac{1}{0.0025} = boiling point {/eq}

- Solve for boiling point: 400.02 K

This can then be converted into degrees Celsius by subtracting 273.15:

- {eq}400.02 - 273.15 = 126.87 {/eq}

Now let's look at another example, where a business wants to use steam from water for energy. They know that they need the temperature to be 254 degrees Fahrenheit to achieve the desired results. What pressure would the system need to be under to reach this temperature?

In this case the same equation is used, but we need to solve for pressure instead of boiling point. First, 254 degrees Fahrenheit needs to be converted into Kelvin. To convert from Fahrenheit to Kelvin we use to following formula:

{eq}Degrees Kelvin = ((Degrees Fahrenheit - 32) \times \frac{5}{9})+273.15 {/eq}

Substitute the known temperature value of 254 degrees Fahrenheit into this formula:

{eq}((254 - 32) \times \frac{5}{9})+273.15 {/eq}

Solving the equation results in a temperature value of 396.5 Kelvin. This value can now be used for boiling point in the logarithmic equation to solve for air pressure:

- {eq}ln \frac{pressure}{101325} = 4890(\frac{1}{373} - \frac{1}{396.5}) {/eq}

- Subtract fractions: {eq}ln \frac{pressure}{101325} = 4890(1.59 \times 10^-4) {/eq}

- Simplify: {eq}ln \frac{pressure}{101325} = 0.777 {/eq}

- Take inverse of natural log: {eq}\frac{pressure}{101325} = e^{0.777} {/eq}

- Multiply both sides by 101325: {eq}pressure = 101325 \times e^{0.777} {/eq}

- Solve for pressure: {eq}pressure = 220375 Pa {/eq}

### How to Calculate Boiling Point of Water at Different Altitudes

To find the boiling point of water at different altitude, first the air pressure at that altitude must be calculated. That new pressure value can then be plugged into the previous equation to find the boiling point. The equation to find air pressure at a specific altitude is:

{eq}P = P_0e^{\frac{-gMh}{RT}} {/eq}

Where:

- P is the new pressure being calculated
- {eq}P_0 {/eq} is the pressure at sea level. This can be in Pascals (101325), atm (1 atm), or psi (14.7 psi)).

- g is the gravitational acceleration. On Earth this is {eq}9.8 m/s^{2} {/eq}

- M is the Molar mass of air. Air on Earth has a Molar mass of 0.03 kg/mol.
- h is the height in meters (or the elevation in meters).
- R is the universal gas constant: {eq}8.31 \frac{N\;m}{mol\;K} {/eq}.

- T is the temperature. The air pressure will change slightly based on the current temperature. To get an exact air pressure the current temperature (in Kelvins) is needed. For general calculations, 288 K can be used.

Inputting each of these numbers the equation (using pascals for pressure) is now:

{eq}P = 101325 e^{\frac{-9.8 \times 0.03 \times h}{8.31 \times 288}} = 101325e ^ {-1.23 \times 10^{-4} h} {/eq}

So, for an elevation of 1500 meters, the air pressure can be calculated as follows:

{eq}P = 101325e ^ {1.23 \times 10^{-4} \times 1500} = 84633 Pa {/eq}

This pressure can then be substituted into the formula for finding boiling point at a specific pressure:

{eq}ln \frac{84633}{101325} = 4890(\frac{1}{373} - \frac{1}{boiling point}) {/eq}

Solving for boiling point at 1500 meter elevation results in a temperature value of 368 K, or 94.9 Celsius.

### How to Calculate Boiling Point of Water with Added Constituents

Whenever a substance is added to water, it will increase the boiling point of the water. This includes substances such as sugar and salt. In order to calculate the new boiling point, a couple of pieces of information are required:

- The molality of the solution (a technical measurement for how much of the compound is in the water)
- The number of particles each compound will form when it dissolves

The equation to calculate the change in temperature is:

{eq}T=1.86\times m \times i {/eq}

Where 'm' is the molality, and 'i' is the number of particles formed.

Let's take a look at 'i' first. For covalent compounds this number is always 1, because covalent compounds do not break apart into smaller parts when dissolved in water. Since sugar is a covalent compound, 'i' for sugar is 1. For ionic compounds, 'i' is the number of ions in the compound, which means the chemical formula is needed. The following examples show how to find 'i' for various substances:

- For salt (NaCl,) the sodium (Na) and the chloride (Cl) each separate to form 2 particles, so 'i' is 2.
- For magnesium chloride, {eq}MgCl_2 {/eq}, it dissolves into 1 magnesium and 2 chloride particles, resulting in 3 particles, so 'i' is 3.

- For potassium nitrate, {eq}KNO_3 {/eq}, the potassium dissolves into one particle, and the nitrate is covalently bonded so it doesn't break apart further, giving just 1 particle for the nitrate as well. This results in a total of 2 particles, and an 'i' value of 2.

In order to calculate molality we need to use stoichiometry, which requires the following information:

- How many grams of substance is added
- How many grams of water there are
- Molar mass of substance added

Consider a scenario in which 15 grams of calcium chloride is added to 100 grams of water. The molar mass of calcium chloride is 110.9 g/mol. Then use the following stoichiometry set up:

{eq}\frac {15g \; Calcium \; Chloride}{100g \; water} \frac {1 \; mol Calcium \; Chloride}{110.9g \; Calcium \; Chloride} \frac {1000g \; water}{1kg \; water} = 1.35 m {/eq}

The chemical formula for calcium chloride is {eq}CaCl_2 {/eq} which means 'i' is equal to 3.

Now that all pieces of required information have been found, the change in boiling point can be determined as follows:

{eq}T = 1.86 \times 1.35 \times 3 = 7.53 {/eq}

This formula calculates the change in degrees Celsius. So, if this scenario was at sea level standard pressure, the normal boiling point of pure water would be 100 degrees Celsius. So to find the new boiling point, add the change in temperature to the regular boiling point to get the new boiling point of 107.53 degrees Celsius.

## Lesson Summary

The boiling point of water can change based on the following factors:

- Elevation
- Air pressure
- Other substances in the water (such as salt and sugar)

Boiling point is when water has reached a critical point, which means:

- the air pressure around the water is equal to the vapor pressure of the water
- the liquid water turns into a gas (steam)
- the temperature of the water does not increase further (additional heat instead converts the water into steam)

To calculate the boiling point with different air pressures use the following formula:

{eq}ln \frac{pressure}{101325} = 4890(\frac{1}{373} - \frac{1}{boiling point}) {/eq}

With pressure in Pascals and boiling point in Kelvin.

To calculate the air pressure at a specific elevation use the following formula:

{eq}P = 101325^ {1.23 \times 10^{-4} h} {/eq}

Where 'h' is the height in meters, and the pressure is in Pascals.

Boiling point changes when substances are added to water. The formula to find the change in boiling point (in degrees Celsius) is:

{eq}T=1.86\times m \times i {/eq}

Where 'm' is the molality of the solution and 'i' is the number of particles the compound dissolves into when it dissolves in the water.

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#### How do you find the boiling point of water at different elevations?

To find the boiling point of water at different elevations, first find the air pressure at that elevation, and then use that air pressure to calculate the boiling point.

#### Does pressure affect the boiling point of water?

Yes. Since the boiling point of water is the temperature at which the vapor pressure of water equals the surrounding air pressure, as air pressure increases the necessary temperature to raise the water's vapor pressure also increases. And as air pressure decreases, the necessary temperature also decreases.

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