Question

State the physical quantity corresponding to each of the following metric units. (a) \(\mathrm{km} / \mathrm{h}\) (b) \(\mathrm{kg} / \mathrm{m}^{3}\) (c) \(J /(k g \times K)\) (d) mol solute/1-L solution

Short answer

(a) Speed, (b) Density, (c) Specific Heat Capacity, (d) Molarity

Step-by-step solution

Analyze Unit for (a)

The unit given is \( \mathrm{km/h} \). This indicates kilometers per hour, which is a measure of speed or velocity. Speed is defined as the distance traveled per unit of time.

Analyze Unit for (b)

The unit given is \( \mathrm{kg/m^3} \). This indicates kilograms per cubic meter, which is a measure of density. Density is defined as the mass per unit volume.

Analyze Unit for (c)

The unit given is \( J/(kg \times K) \). This indicates joules per kilogram per Kelvin, which is a measure of specific heat capacity. Specific heat capacity is defined as the amount of heat needed to change the temperature of a unit mass of a substance by one degree Kelvin.

Analyze Unit for (d)

The unit given is mol solute/1-L solution. This refers to mole per liter, which is a measure of concentration. Specifically, it is known as molarity, which indicates the number of moles of solute per liter of solution.

Key concepts

Speed

Speed, often represented in units such as kilometers per hour (\(\mathrm{km/h}\)), is a fundamental concept of motion. It describes how fast an object travels over a specific distance. In scientific terms, speed is calculated as the distance an object moves divided by the time it takes to move that distance.

• Formula: Speed = Distance/Time
• Example: A car that covers 100 kilometers in 2 hours has a speed of 50 km/h.

Speed is a scalar quantity, meaning it only deals with magnitude (how fast), but not direction. This makes it different from velocity, which is a vector quantity and includes both speed and direction. For instance, saying a car is moving at 60 km/h tells us the speed, but saying it is moving at 60 km/h north gives us the velocity.

Density

Density is a measure of how much mass is contained in a given volume, typically expressed in kilograms per cubic meter (\(\mathrm{kg/m^3}\)). Understanding density involves not only how heavy an object is but how much space it occupies.

• Formula: Density = Mass/Volume
• Example: If a block of wood has a mass of 200 kg and occupies a space of 0.5 \(\mathrm{m^3}\), its density is 400 \(\mathrm{kg/m^3}\).

Density plays a crucial role in determining whether an object will float or sink when placed in a fluid. Objects with densities less than the fluid will float, while those with greater densities will sink. This principle is essential in fields ranging from material science to fluid dynamics.

Specific Heat Capacity

Specific heat capacity is a measure of how much heat energy is required to raise the temperature of one kilogram of a substance by one degree Kelvin. It is expressed in joules per kilogram per Kelvin (\(J/(kg \times K)\)).

• Formula: \( q = mc\Delta T \) (where \( q \) = heat energy, \( m \) = mass, \( c \) = specific heat capacity, and \( \Delta T \) = change in temperature)
• Example: Water has a high specific heat capacity of approximately 4184 \(J/(kg \times K)\), meaning it takes a lot of energy to increase its temperature.

Specific heat capacity is a critical factor in climate science, engineering, and culinary arts, as it determines how substances respond to heat. A higher specific heat capacity means a material can absorb more heat without experiencing a significant increase in temperature.

Concentration

Concentration refers to the abundance of a constituent (usually a solute) within a mixture or solution. Molarity, a common unit of concentration, is measured in moles of solute per liter of solution (mol/L).

• Formula: Molarity (M) = Moles of solute / Liters of solution
• Example: If you dissolve 1 mole of sugar in 1 liter of water, the concentration (molarity) is 1 M.

Understanding concentration is crucial in chemistry, especially when performing reactions that require specific solute-to-solvent ratios. It helps chemists understand how reactions occur at the molecular level and predict the outcomes of chemical interactions. In industries, controlling concentration is vital for consistency in product manufacturing.