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42-601: Under these conditions, essentially all molecules which arrive at the hole continue and pass through the hole, since collisions between molecules in the region of the hole are negligible. Conversely, when the diameter is larger than the mean free path of the gas, flow obeys the Sampson flow law. In medical terminology, an effusion refers to accumulation of fluid in an anatomic space , usually without loculation . Specific examples include subdural , mastoid , pericardial and pleural effusions . The word effusion derives from

84-421: A v g ≈ 1.085   v a v g {\textstyle v_{\rm {rms}}={\sqrt {3\pi /8}}\ v_{\rm {avg}}\approx 1.085\ v_{\rm {avg}}} ). The rate Φ N {\displaystyle \Phi _{N}} at which a gas of molar mass M {\displaystyle M} effuses (typically expressed as the number of molecules passing through

126-425: A chemical compound is defined as the ratio between the mass and the amount of substance (measured in moles ) of any sample of the compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes . Most commonly, the molar mass is computed from the standard atomic weights and

168-419: A molality , the proportionality constant is known as the cryoscopic constant ( K f ) and is characteristic for each solvent. If w represents the mass fraction of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by The boiling point of a solution of an involatile solute is higher than that of the pure solvent , and the boiling-point elevation ( Δ T )

210-409: A compound in g/mol thus is equal to the mass of this number of molecules of the compound in grams. The molar mass of atoms of an element is given by the relative atomic mass of the element multiplied by the molar mass constant , M u  ≈  1.000 000 × 10  kg/mol = 1 g/mol. For normal samples from earth with typical isotope composition, the atomic weight can be approximated by

252-416: A gas is inversely proportional to the square root of the mass of its particles. In other words, the ratio of the rates of effusion of two gases at the same temperature and pressure is given by the inverse ratio of the square roots of the masses of the gas particles. where M 1 {\displaystyle M_{1}} and M 2 {\displaystyle M_{2}} represent

294-420: A precision of a few parts per million . This is accurate enough to directly determine the chemical formula of a molecule. The term formula weight has a specific meaning when used in the context of DNA synthesis: whereas an individual phosphoramidite nucleobase to be added to a DNA polymer has protecting groups and has its molecular weight quoted including these groups, the amount of molecular weight that

336-414: A sample which has been distilled will be enriched in the lighter isotopes of all the elements present. This complicates the calculation of the standard uncertainty in the molar mass. A useful convention for normal laboratory work is to quote molar masses to two decimal places for all calculations. This is more accurate than is usually required, but avoids rounding errors during calculations. When

378-526: A separate dimension of measurement . Until 2019, the mole was defined as the amount of substance that has as many constituent particles as there are atoms in 12 grams of carbon-12 . During that period, the molar mass of carbon-12 was thus exactly 12 g/mol, by definition. Since 2019, a mole of any substance has been redefined in the SI as the amount of that substance containing an exactly defined number of particles, 6.022 140 76 × 10 . The molar mass of

420-474: A vapor at low pressure by sublimation . The vapor slowly effuses through a pinhole, and the loss of mass is proportional to the vapor pressure and can be used to determine this pressure. The heat of sublimation can also be determined by measuring the vapor pressure as a function of temperature, using the Clausius–Clapeyron relation . Mean free path Too Many Requests If you report this error to

462-414: A volumetric flow rate as follows: or where Φ V {\displaystyle \Phi _{V}} is the volumetric flow rate of the gas, P a v g {\displaystyle P_{\rm {avg}}} is the average pressure on either side of the orifice, and d {\displaystyle d} is the hole diameter. At constant pressure and temperature,

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504-451: Is distinct but related to the molar mass, which is a measure of the average molecular mass of all the molecules in a sample and is usually the more appropriate measure when dealing with macroscopic (weigh-able) quantities of a substance. Molecular masses are calculated from the atomic masses of each nuclide , while molar masses are calculated from the standard atomic weights of each element . The standard atomic weight takes into account

546-405: Is given by Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known pressure and temperature : The freezing point of a solution is lower than that of the pure solvent , and the freezing-point depression ( Δ T ) is directly proportional to the amount concentration for dilute solutions. When the composition is expressed as

588-447: Is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol. The mole was defined in such a way that the molar mass of a compound, in g/mol, is numerically equal to the average mass of one molecule or formula unit, in daltons. It was exactly equal before the redefinition of the mole in 2019 , and is now only approximately equal, but the difference is negligible for all practical purposes. Thus, for example,

630-436: Is limited by the knowledge of the isotopic distribution of the element. If a more accurate value of the molar mass is required, it is necessary to determine the isotopic distribution of the sample in question, which may be different from the standard distribution used to calculate the standard atomic mass. The isotopic distributions of the different elements in a sample are not necessarily independent of one another: for example,

672-784: Is much greater than pinhole diameter and the gas can be treated as an ideal gas . If a small area A {\displaystyle A} on the container is punched to become a small hole, the effusive flow rate will be Q effusion = J impingement × A = P A 2 π m k B T = P A N A 2 π M R T {\displaystyle {\begin{aligned}Q_{\text{effusion}}&=J_{\text{impingement}}\times A\\&={\frac {PA}{\sqrt {2\pi mk_{\text{B}}T}}}\\&={\frac {PAN_{\text{A}}}{\sqrt {2\pi MRT}}}\end{aligned}}} where M {\displaystyle M}

714-461: Is particularly important in polymer science , where there is usually a molar mass distribution of non-uniform polymers so that different polymer molecules contain different numbers of monomer units. The average molar mass of mixtures M ¯ {\displaystyle {\overline {M}}} can be calculated from the mole fractions x i of the components and their molar masses M i : It can also be calculated from

756-640: Is the Boltzmann constant . The average molecular speed can be calculated from the Maxwell speed distribution as v a v g = 8 / 3 π   v r m s ≈ 0.921   v r m s {\textstyle v_{\rm {avg}}={\sqrt {8/3\pi }}\ v_{\rm {rms}}\approx 0.921\ v_{\rm {rms}}} (or, equivalently, v r m s = 3 π / 8   v

798-432: Is the absolute temperature . Assuming the pressure difference between the two sides of the barrier is much smaller than P a v g {\displaystyle P_{\rm {avg}}} , the average absolute pressure in the system ( i.e. Δ P ≪ P a v g {\displaystyle \Delta P\ll P_{\rm {avg}}} ), it is possible to express effusion flow as

840-811: Is the molar mass , N A {\displaystyle N_{\text{A}}} is the Avogadro constant , and R = N A k B {\displaystyle R=N_{\text{A}}k_{\text{B}}} is the molar gas constant . The average velocity of effused particles is v x ¯ = v y ¯ = 0 v z ¯ = π k B T 2 m . {\displaystyle {\begin{aligned}{\overline {v_{x}}}&={\overline {v_{y}}}=0\\{\overline {v_{z}}}&={\sqrt {\frac {\pi k_{\text{B}}T}{2m}}}.\end{aligned}}} Combined with

882-538: Is the mass of one molecule (of any single isotopic composition), and to the atomic mass , which is the mass of one atom (of any single isotope). The dalton , symbol Da, is also sometimes used as a unit of molar mass, especially in biochemistry , with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u = 1.660 539 068 92 (52) × 10  kg , as of 2022 CODATA recommended values). Obsolete terms for molar mass include gram atomic mass for

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924-397: Is the molar mass of the atoms multiplied by the number of atoms in each molecule: The molar mass of a compound is given by the sum of the relative atomic mass A r of the atoms which form the compound multiplied by the molar mass constant M u ≈ 1  g/mol {\displaystyle M_{u}\approx 1{\text{ g/mol}}} : Here, M r

966-1312: Is the relative molar mass, also called formula weight. For normal samples from earth with typical isotope composition, the standard atomic weight or the conventional atomic weight can be used as an approximation of the relative atomic mass of the sample. Examples are: M ( NaCl ) = [ 22.98976928 ( 2 ) + 35.453 ( 2 ) ] × 1  g/mol = 58.443 ( 2 )  g/mol M ( C 12 H 22 O 11 ) = [ 12 × 12.0107 ( 8 ) + 22 × 1.00794 ( 7 ) + 11 × 15.9994 ( 3 ) ] × 1  g/mol = 342.297 ( 14 )  g/mol {\displaystyle {\begin{array}{ll}M({\ce {NaCl}})&={\bigl [}22.98976928(2)+35.453(2){\bigr ]}\times 1{\text{ g/mol}}\\&=58.443(2){\text{ g/mol}}\\[4pt]M({\ce {C12H22O11}})&={\bigl [}12\times 12.0107(8)+22\times 1.00794(7)+11\times 15.9994(3){\bigr ]}\times 1{\text{ g/mol}}\\&=342.297(14){\text{ g/mol}}\end{array}}} An average molar mass may be defined for mixtures of compounds. This

1008-470: Is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities. The molecular mass (for molecular compounds) and formula mass (for non-molecular compounds, such as ionic salts ) are commonly used as synonyms of molar mass, differing only in units ( daltons vs g/mol); however,

1050-457: Is ultimately added by this nucleobase to a DNA polymer is referred to as the nucleobase's formula weight (i.e., the molecular weight of this nucleobase within the DNA polymer, minus protecting groups). The precision to which a molar mass is known depends on the precision of the atomic masses from which it was calculated (and very slightly on the value of the molar mass constant , which depends on

1092-621: The Latin word, effundo, which means "shed", "pour forth", "pour out", "utter", "lavish", "waste". Effusion from an equilibrated container into outside vacuum can be calculated based on kinetic theory . The number of atomic or molecular collisions with a wall of a container per unit area per unit time ( impingement rate ) is given by: J impingement = P 2 π m k B T . {\displaystyle J_{\text{impingement}}={\frac {P}{\sqrt {2\pi mk_{\text{B}}T}}}.} assuming mean free path

1134-487: The isotopic distribution of the element in a given sample (usually assumed to be "normal"). For example, water has a molar mass of 18.0153(3) g/mol , but individual water molecules have molecular masses which range between 18.010 564 6863 (15) Da ( H 2 O ) and 22.027 7364 (9) Da ( H 2 O ). The distinction between molar mass and molecular mass is important because relative molecular masses can be measured directly by mass spectrometry , often to

1176-414: The kinetic theory of gases , the kinetic energy for a gas at a temperature T {\displaystyle T} is where m {\displaystyle m} is the mass of one molecule, v r m s {\displaystyle v_{\rm {rms}}} is the root-mean-square speed of the molecules, and k B {\displaystyle k_{\rm {B}}}

1218-411: The mass fractions w i of the components: As an example, the average molar mass of dry air is 28.96 g/mol. Molar mass is closely related to the relative molar mass ( M r ) of a compound and to the standard atomic weights of its constituent elements. However, it should be distinguished from the molecular mass (which is confusingly also sometimes known as molecular weight), which

1260-422: The relative molar mass ( M r ). This is a dimensionless quantity (i.e., a pure number, without units) equal to the molar mass divided by the molar mass constant . The molecular mass ( m ) is the mass of a given molecule: it is usually measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. This

1302-488: The Wikimedia System Administrators, please include the details below. Request from 172.68.168.226 via cp1108 cp1108, Varnish XID 197930535 Upstream caches: cp1108 int Error: 429, Too Many Requests at Thu, 28 Nov 2024 05:39:12 GMT Molar mass In chemistry , the molar mass ( M ) (sometimes called molecular weight or formula weight , but see related quantities for usage) of

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1344-413: The average mass of a molecule of water is about 18.0153 daltons, and the molar mass of water is about 18.0153 g/mol. For chemical elements without isolated molecules, such as carbon and metals, the molar mass is computed dividing by the number of moles of atoms instead. Thus, for example, the molar mass of iron is about 55.845 g/mol. Since 1971, SI defined the "amount of substance" as

1386-407: The effusive flow rate, the recoil/thrust force on the system itself is F = m v z ¯ × Q effusion = P A 2 . {\displaystyle F=m{\overline {v_{z}}}{\times }Q_{\text{effusion}}={\frac {PA}{2}}.} An example is the recoil force on a balloon with a small hole flying in vacuum. According to

1428-431: The hole per second) is then Here Δ P {\displaystyle \Delta P} is the gas pressure difference across the barrier, A {\displaystyle A} is the area of the hole, N A {\displaystyle N_{\text{A}}} is the Avogadro constant , R {\displaystyle R} is the gas constant and T {\displaystyle T}

1470-412: The mass, in grams, of one mole of atoms of an element, and gram molecular mass for the mass, in grams, of one mole of molecules of a compound. The gram-atom is a former term for a mole of atoms, and gram-molecule for a mole of molecules. Molecular weight (M.W.) (for molecular compounds) and formula weight (F.W.) (for non-molecular compounds), are older terms for what is now more correctly called

1512-428: The measured value of the dalton ). Most atomic masses are known to a precision of at least one part in ten-thousand, often much better (the atomic mass of lithium is a notable, and serious, exception). This is adequate for almost all normal uses in chemistry: it is more precise than most chemical analyses , and exceeds the purity of most laboratory reagents. The precision of atomic masses, and hence of molar masses,

1554-703: The molar mass is greater than 1000 g/mol, it is rarely appropriate to use more than one decimal place. These conventions are followed in most tabulated values of molar masses. Molar masses are almost never measured directly. They may be calculated from standard atomic masses, and are often listed in chemical catalogues and on safety data sheets (SDS). Molar masses typically vary between: While molar masses are almost always, in practice, calculated from atomic weights, they can also be measured in certain cases. Such measurements are much less precise than modern mass spectrometric measurements of atomic weights and molecular masses, and are of mostly historical interest. All of

1596-406: The molar masses of the gases. This equation is known as Graham's law of effusion . The effusion rate for a gas depends directly on the average velocity of its particles. Thus, the faster the gas particles are moving, the more likely they are to pass through the effusion orifice. The Knudsen cell is used to measure the vapor pressures of a solid with very low vapor pressure. Such a solid forms

1638-470: The most authoritative sources define it differently. The difference is that molecular mass is the mass of one specific particle or molecule, while the molar mass is an average over many particles or molecules. The molar mass is an intensive property of the substance, that does not depend on the size of the sample. In the International System of Units (SI), the coherent unit of molar mass

1680-443: The procedures rely on colligative properties , and any dissociation of the compound must be taken into account. The measurement of molar mass by vapour density relies on the principle, first enunciated by Amedeo Avogadro , that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in the ideal gas equation : where n is the amount of substance . The vapour density ( ρ )

1722-418: The root-mean-square speed and therefore the effusion rate are inversely proportional to the square root of the molecular weight. Gases with a lower molecular weight effuse more rapidly than gases with a higher molecular weight, so that the number of lighter molecules passing through the hole per unit time is greater. Scottish chemist Thomas Graham (1805–1869) found experimentally that the rate of effusion of

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1764-486: The standard atomic weight or the conventional atomic weight. Multiplying by the molar mass constant ensures that the calculation is dimensionally correct: standard relative atomic masses are dimensionless quantities (i.e., pure numbers) whereas molar masses have units (in this case, grams per mole). Some elements are usually encountered as molecules , e.g. hydrogen ( H 2 ), sulfur ( S 8 ), chlorine ( Cl 2 ). The molar mass of molecules of these elements

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