What is the edge length (in cm) of a titanium cube that contains 2.55 * 1024 titanium atoms? The density of titanium is 4.50 g/cm³.

검증된 단계별 안내

Determine the molar mass of titanium (Ti) from the periodic table, which is approximately 47.87 g/mol.

Calculate the number of moles of titanium atoms using Avogadro's number (6.022 \(\times\) 10^{23} atoms/mol) by dividing the given number of atoms (2.55 \(\times\) 10^{24}) by Avogadro's number.

Convert the moles of titanium to grams using the molar mass of titanium.

Use the density formula, density = mass/volume, to find the volume of the titanium cube by rearranging it to volume = mass/density.

Calculate the edge length of the cube by taking the cube root of the volume, since volume of a cube = edge length^3.

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주요 개념

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

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of atoms, ions, or molecules in one mole of a substance. This concept is essential for converting between the number of atoms and the amount of substance in moles, allowing us to relate the number of titanium atoms in the cube to its mass.

Density

Density is defined as mass per unit volume and is typically expressed in grams per cubic centimeter (g/cm³) for solids. In this problem, the density of titanium (4.50 g/cm³) is used to calculate the mass of the titanium cube, which is necessary for determining its volume and subsequently its edge length.

Volume of a Cube

The volume of a cube is calculated using the formula V = a³, where 'a' is the length of one edge of the cube. Once the mass of the titanium is determined from the number of atoms and density, the volume can be calculated, allowing us to solve for the edge length of the cube.

What is the edge length (in cm) of a titanium cube that contains 2.55 * 1024 titanium atoms? The density of titanium is 4.50 g/cm3.