An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Convert the volume from liters to cubic centimeters: 0.816 L = 816 c m 3 .
Calculate the density using the formula d e n s i t y = v o l u m e ma ss = 816 c m 3 762 g = 0.93382352941 c m 3 g .
Round the density to 3 significant digits: d e n s i t y ≈ 0.934 c m 3 g .
Identify the liquid by comparing the calculated density to the given densities: the liquid is methyl acetate.
The density of the liquid is 0.934 c m 3 g , and the liquid is methyl acetate. 0.934
Explanation
Problem Analysis We are given the mass and volume of an unknown liquid and asked to calculate its density and identify it from a list of known liquids.
Volume Conversion First, we need to convert the volume of the unknown liquid from liters (L) to cubic centimeters ( c m 3 ). We know that 1 L = 1000 c m 3 . Therefore, the volume in cubic centimeters is: 0.816 L × 1000 L c m 3 = 816 c m 3
Density Calculation Next, we calculate the density of the unknown liquid using the formula: d e n s i t y = v o l u m e ma ss We have the mass as 762 g and the volume as 816 c m 3 . Thus, d e n s i t y = 816 c m 3 762 g = 0.93382352941 c m 3 g
Rounding the Density Now, we round the calculated density to 3 significant digits: d e n s i t y ≈ 0.934 c m 3 g
Identifying the Liquid Finally, we compare the calculated density to the densities of the known liquids:
dimethyl sulfoxide: 1.1 g / c m 3
chloroform: 1.5 g / c m 3
pentane: 0.63 g / c m 3
diethylamine: 0.71 g / c m 3
methyl acetate: 0.93 g / c m 3 The calculated density (0.934 g / c m 3 ) is closest to the density of methyl acetate (0.93 g / c m 3 ).
Final Answer Therefore, the density of the unknown liquid is approximately 0.934 g / c m 3 , and it is possible to identify the liquid as methyl acetate.
Examples
Understanding density is crucial in many real-world applications. For instance, when designing ships, engineers need to calculate the density of materials to ensure buoyancy. Similarly, in the food industry, density is used to determine the purity and concentration of various substances. Knowing the density of liquids helps in identifying substances, calculating their mass from volume, and understanding their behavior in different conditions. For example, if you have 100 c m 3 of methyl acetate, you can calculate its mass using the density: ma ss = d e n s i t y × v o l u m e = 0.93 c m 3 g × 100 c m 3 = 93 g .
The number of electrons flowing through an electric device delivering 15.0 A for 30 seconds is approximately 2.81 × 1 0 21 electrons. This is calculated using the relationship between current, charge, and time, alongside the charge of an electron. Understanding these concepts illustrates how electric charge is quantified in terms of the flow of electrons.
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