Skip to main content
Ch.1 - Introduction: Matter, Energy, and Measurement
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Brown 15th EditionCh.1 - Introduction: Matter, Energy, and Measurement문제 40c
1장, 문제 40c

The density of titanium metal is 4.506 g/cm3 at 20 °C. What is the mass of a spherical ball of titanium with a diameter of 2.00 cm. [The volume of a sphere is (4/3) πr3, where r is the radius.]

검증된 단계별 안내
1
Calculate the radius of the sphere by dividing the diameter by 2: r = \(\frac{2.00 \text{ cm}\)}{2}.
Use the formula for the volume of a sphere: V = \(\frac{4}{3}\) \(\pi\) r^3, substituting the radius you calculated.
Calculate the volume of the sphere using the value of \(\pi\) \(\approx\) 3.14159.
Use the density formula, \(\text{Density}\) = \(\frac{\text{Mass}\)}{\(\text{Volume}\)}, to solve for mass: \(\text{Mass}\) = \(\text{Density}\) \(\times\) \(\text{Volume}\).
Substitute the given density of titanium and the calculated volume into the formula to find the mass of the titanium sphere.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) for solids. It is a crucial property that helps determine how much mass is contained in a given volume of a substance. In this problem, the density of titanium is provided, which will be used to calculate the mass of the spherical ball once its volume is determined.
추천 영상:
가이드 코스
01:56
Density Concepts

Volume of a Sphere

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. This formula is essential for determining how much space the spherical ball occupies. In this case, the diameter is given, so the radius must be calculated by dividing the diameter by two before applying the formula.
추천 영상:
가이드 코스
02:35
Constant-Volume Calorimetry

Mass Calculation

Mass can be calculated using the formula mass = density × volume. Once the volume of the titanium sphere is determined using the volume formula, this relationship allows us to find the mass by multiplying the volume by the density of titanium. This step is critical for solving the problem and finding the mass of the spherical ball.
추천 영상:
가이드 코스
03:12
Molar Mass Calculation Example
관련 실천
교과서 질문

a. After the label fell off a bottle containing a clear liquid believed to be a solvent called tetrahydrofuran, a chemist measured the density of the liquid to verify its identity. A 25.0-mL portion of the liquid had a mass of 22.08 g. A chemistry handbook lists the density of tetrahydrofuran at 25 °C as 0.8833 g/mL. Is the calculated density in agreement with the tabulated value?

3
views
교과서 질문

For January through April 2020, at the height of the global coronavirus pandemic, it is estimated that global emissions of carbon dioxide (CO2) decreased by 940 million metric tons (1 metric ) compared to the same period in 2019. a. Express this mass of CO2 in grams without exponential notation, using an appropriate metric prefix.

2
views
교과서 질문

b. An experiment requires 50.0 g of a substance called n-hexane, whose density at 25 °C is 0.6606 g/mL. What volume of n-hexane should be used?

4
views
교과서 질문

Indicate which of the following are exact numbers: (a) the mass of a 32-oz bag of sugar, (b) the number of students in your chemistry class, (c) the temperature of the surface of the Sun, (d) the mass of a postage stamp, (e) the number of milliliters in a cubic meter of water, (f) the average height of NBA basketball players.

3
views
교과서 질문

(d) A cubic piece of metal measures 5.00 cm on each edge. If the metal is nickel, whose density is 8.90 g/cm3, what is the mass of the cube?

1450
views
1
rank
교과서 질문

Indicate which of the following are exact numbers: (a) the mass of a 3- by 5-in. index card, (b) the number of ounces in a pound, (c) the volume of a cup of Seattle's Best coffee, (d) the number of inches in a mile, (e) the number of microseconds in a week, (f) the number of pages in this book.

958
views