The Rankine temperature scale used in engineering is to the Fahrenheit scale as the Kelvin scale is to the Celsius scale. That is, 1 Rankine degree is the same size as 1 Fahrenheit degree, and 0 °R = absolute zero. (a) What temperature corresponds to the freezing point of water on the Rankine scale?
Ch.1 - Chemical Tools: Experimentation & Measurement
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McMurry 8th Edition
Ch.1 - Chemical Tools: Experimentation & Measurement
Problema 119b
McMurry 8th Edition
Ch.1 - Chemical Tools: Experimentation & Measurement
Problema 119bCapitolo 1, Problema 119b
The element gallium (Ga) has the second-largest liquid range of any element, melting at 29.78 °C and boiling at 2204 °C at atmospheric pressure. (b) Assume that you construct a thermometer using gallium as the fluid instead of mercury and that you define the melting point of gallium as 0 °G and the boiling point of gallium as 1000 °G. What is the melting point of sodium chloride (801 °C) on the gallium scale?
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Identify the melting and boiling points of gallium on the Celsius scale: melting point = 29.78 °C, boiling point = 2204 °C.
Set up the gallium temperature scale where 0 °G corresponds to 29.78 °C and 1000 °G corresponds to 2204 °C.
Calculate the range of temperatures on the Celsius scale that corresponds to the gallium scale: 2204 °C - 29.78 °C.
Determine the conversion factor from the Celsius scale to the gallium scale by dividing the range in °G by the range in °C.
Apply the conversion factor to the melting point of sodium chloride (801 °C) to find its equivalent on the gallium scale.

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Melting and Boiling Points
Melting and boiling points are critical physical properties of substances that indicate the temperatures at which a solid becomes a liquid and a liquid becomes a gas, respectively. For gallium, the melting point is 29.78 °C and the boiling point is 2204 °C. These points are essential for understanding how to scale temperatures in a thermometer using gallium as the fluid.
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Temperature Scales
Temperature scales are systems for measuring temperature, with Celsius and Fahrenheit being the most common. In this scenario, a new scale is defined where gallium's melting point is set to 0 °G and its boiling point to 1000 °G. Understanding how to convert temperatures between different scales is crucial for determining the melting point of sodium chloride on the gallium scale.
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Linear Interpolation
Linear interpolation is a mathematical method used to estimate unknown values that fall within a range of known values. In this case, to find the melting point of sodium chloride on the gallium scale, one can use the known melting and boiling points of gallium to create a linear relationship. This technique allows for the conversion of sodium chloride's temperature from Celsius to the defined gallium scale.
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