Tetrasodium tetra­hydro­furan-trans-cis-trans-tetra­carboxyl­ate pentahydrate

In Na₄[C₄H₄O(COO)₄]·5H₂O (or 4Na⁺·C₈H₄O₉^4-·5H₂O), the anions are connected by hydrogen bonds to water mol­ecules to form bilayers of open columns. Three of the sodium ions are located inside these columns. The final sodium ion interconnects the bilayers of anions. Three of the sodium ions have distorted octahedral coordination, the other has a trigonal pyramidal environment. The ligands are O atoms belonging to water, carboxyl­ate groups or, in one case, the furan ring. The Na-O distances are between 2.303 (2) and 2.596 (3) Å.

Key indicators

• Single-crystal X-ray study
• T = 150 K
• Mean [sigma](C-C) = 0.004 Å
• R factor = 0.052
• wR factor = 0.145
• Data-to-parameter ratio = 13.6

checkCIF results

No syntax errors found

ADDSYM reports no extra symmetry


 Alert Level C:



PLAT_354  Alert C Short O-H Bond (0.82A)     O(25)  -   H(25A) =       0.68 Ang.

PLAT_354  Alert C Short O-H Bond (0.82A)     O(23)  -   H(23B) =       0.68 Ang.


 0 Alert Level A = Potentially serious problem

 0 Alert Level B = Potential problem

 2 Alert Level C = Please check

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Computing details

Data collection: DENZO (Otwinowski & Minor, 1997) and COLLECT (Hooft, 1998); cell refinement: DENZO and COLLECT; data reduction: DENZO and COLLECT; program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: PLATON (Spek, 1999); software used to prepare material for publication: SHELXL97.

Tetrasodium tetrahydrofuran-trans-cis-trans-tetracarboxylate pentahydrate

Crystal data

4Na^+·C8H4O9^4^−·5H2O	F(000) = 1744
Mr = 426.15	Dx = 1.867 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 30.1575 (13) Å	Cell parameters from 10138 reflections
b = 6.3341 (3) Å	θ = 2.9–33.7°
c = 15.9844 (9) Å	µ = 0.27 mm^−1
β = 96.772 (2)°	T = 150 K
V = 3032.0 (3) Å^3	Plate, colourless
Z = 8	0.10 × 0.05 × 0.02 mm

Data collection

Enraf-Nonius KappaCCD area-detector diffractometer	3594 independent reflections
Radiation source: Enraf-Nonius FR591 rotating anode	2389 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.055
Detector resolution: 9.091 pixels mm^-1	θmax = 28.0°, θmin = 3.0°
φ and ω scans	h = −39→39
Absorption correction: multi-scan (SORTAV; Blessing, 1995)	k = −7→8
Tmin = 0.940, Tmax = 0.976	l = −20→17
12544 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.052	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.145	H atoms treated by a mixture of independent and constrained refinement
S = 1.02	w = 1/[σ^2(Fo^2) + (0.076P)^2 + 0.1007P] where P = (Fo^2 + 2Fc^2)/3
3594 reflections	(Δ/σ)max = 0.001
265 parameters	Δρmax = 0.82 e Å^−3
0 restraints	Δρmin = −0.34 e Å^−3

Special details

Experimental. PLEASE NOTE cell_measurement_ fields are not relevant to area detector data, the entire data set is used to refine the cell, which is indexed from all observed reflections in a 10 degree phi range.

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Hydrogen atoms attached to carbon were placed on calculated positions and allowed to ride on the adjacent carbon atom during refinement. Isotropic displacement parameters were constrained to be 1.3 times the U(eq) of the adjacent carbon atom. Hydrogen atoms of the water molecules were located on a difference synthesis. Positional parameters were refined without constraint, this allowed H23B and H25A to refine to positions unreasonably close to O23 and O25 respectively (0.67 (3), 0.68 (3) Å). No attempt has been made to adjust these artificially. The isotropic displacement parameters of all the hydrogen atoms of water molecules were fixed at 0.025.

The final difference synthesis showed a residual peak of 0.82 e/ų. This feature lies over the furan ring, at 1.265 Šfrom O1 and 2.10 Šfrom Na1. This position is not chemically meaningful and is not consistent with disorder of the ring conformation. The biggest negative feature is -0.34 e/ų at 0.73 Šfrom Na1.

Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Na1	0.16280 (3)	0.98237 (16)	0.38398 (7)	0.0240 (3)
Na2	0.23534 (3)	0.52485 (16)	0.44398 (7)	0.0225 (3)
Na3	0.01097 (3)	0.64696 (16)	0.09366 (7)	0.0238 (3)
Na4	0.11308 (3)	0.45239 (16)	0.40245 (7)	0.0245 (3)
O1	0.11944 (6)	0.8759 (3)	0.75602 (12)	0.0237 (4)
C2	0.09676 (9)	1.0277 (4)	0.70010 (17)	0.0222 (6)
H2	0.0679	0.9681	0.6731	0.029*
C3	0.12797 (9)	1.0723 (4)	0.63325 (17)	0.0234 (6)
H3	0.1463	1.1987	0.6523	0.030*
C4	0.16035 (9)	0.8766 (4)	0.63779 (17)	0.0221 (6)
H4	0.1912	0.9236	0.6597	0.029*
C5	0.14187 (8)	0.7367 (4)	0.70409 (17)	0.0221 (6)
H5	0.1198	0.6346	0.6753	0.029*
C6	0.08833 (9)	1.2274 (4)	0.74858 (17)	0.0212 (6)
O7	0.06324 (6)	1.3598 (3)	0.71028 (12)	0.0274 (5)
O8	0.10635 (6)	1.2429 (3)	0.82339 (12)	0.0257 (4)
C9	0.10418 (9)	1.1211 (4)	0.54456 (18)	0.0212 (6)
O10	0.06238 (6)	1.1261 (3)	0.53192 (12)	0.0262 (5)
O11	0.12965 (6)	1.1623 (3)	0.48980 (11)	0.0220 (4)
C12	0.16151 (8)	0.7646 (4)	0.55202 (16)	0.0192 (6)
O13	0.12831 (6)	0.6626 (3)	0.52215 (12)	0.0268 (5)
O14	0.19626 (6)	0.7899 (3)	0.51684 (12)	0.0229 (4)
C15	0.17768 (8)	0.6163 (4)	0.75911 (17)	0.0200 (6)
O16	0.18135 (6)	0.6397 (3)	0.83735 (12)	0.0220 (4)
O17	0.20057 (6)	0.4915 (3)	0.71919 (12)	0.0220 (4)
O21	0.21520 (7)	0.7081 (3)	0.05842 (13)	0.0247 (4)
O22	0.03764 (6)	0.4140 (3)	0.34185 (13)	0.0262 (5)
O23	0.02890 (7)	0.9778 (3)	0.37894 (15)	0.0294 (5)
O24	0.03875 (7)	0.6649 (3)	0.53727 (14)	0.0277 (5)
O25	0.22221 (7)	0.8209 (4)	0.33149 (14)	0.0319 (5)
H21A	0.1889 (11)	0.745 (5)	0.0349 (19)	0.030*
H21B	0.2097 (10)	0.641 (5)	0.098 (2)	0.030*
H22A	0.0288 (10)	0.290 (5)	0.3392 (19)	0.030*
H22B	0.0427 (10)	0.452 (5)	0.295 (2)	0.030*
H23A	0.0412 (10)	1.039 (5)	0.432 (2)	0.030*
H23B	0.0481 (12)	0.941 (6)	0.366 (2)	0.030*
H24A	0.0365 (11)	0.781 (5)	0.553 (2)	0.030*
H24B	0.0655 (11)	0.670 (5)	0.534 (2)	0.030*
H25A	0.2396 (11)	0.877 (5)	0.320 (2)	0.030*
H25B	0.2164 (10)	0.721 (5)	0.293 (2)	0.030*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.0259 (6)	0.0254 (6)	0.0207 (6)	0.0011 (4)	0.0032 (5)	−0.0026 (4)
Na2	0.0219 (5)	0.0212 (5)	0.0245 (6)	−0.0017 (4)	0.0035 (4)	−0.0031 (4)
Na3	0.0226 (5)	0.0227 (6)	0.0260 (6)	−0.0013 (4)	0.0017 (4)	−0.0018 (4)
Na4	0.0249 (5)	0.0214 (5)	0.0270 (6)	0.0028 (4)	0.0028 (5)	0.0048 (5)
O1	0.0282 (10)	0.0217 (10)	0.0220 (10)	0.0050 (8)	0.0060 (8)	0.0006 (8)
C2	0.0227 (13)	0.0222 (14)	0.0215 (15)	0.0023 (11)	0.0024 (11)	0.0015 (11)
C3	0.0280 (14)	0.0199 (13)	0.0228 (15)	0.0037 (12)	0.0054 (12)	−0.0002 (11)
C4	0.0232 (13)	0.0202 (14)	0.0233 (15)	0.0032 (11)	0.0050 (11)	0.0012 (11)
C5	0.0246 (13)	0.0199 (13)	0.0230 (15)	0.0005 (11)	0.0075 (11)	−0.0015 (11)
C6	0.0225 (12)	0.0194 (13)	0.0224 (15)	−0.0015 (11)	0.0057 (11)	−0.0022 (11)
O7	0.0324 (10)	0.0222 (10)	0.0264 (11)	0.0087 (9)	−0.0019 (9)	−0.0018 (8)
O8	0.0293 (10)	0.0232 (10)	0.0233 (11)	0.0048 (8)	−0.0022 (8)	−0.0060 (8)
C9	0.0283 (14)	0.0139 (12)	0.0218 (15)	0.0049 (11)	0.0040 (12)	0.0003 (11)
O10	0.0231 (9)	0.0291 (11)	0.0271 (11)	0.0058 (8)	0.0053 (8)	0.0007 (8)
O11	0.0249 (9)	0.0212 (9)	0.0202 (10)	0.0011 (8)	0.0042 (8)	0.0021 (8)
C12	0.0241 (13)	0.0120 (12)	0.0213 (14)	0.0041 (11)	0.0021 (11)	0.0024 (10)
O13	0.0244 (10)	0.0247 (10)	0.0316 (12)	−0.0045 (8)	0.0041 (9)	−0.0046 (8)
O14	0.0217 (9)	0.0214 (10)	0.0268 (11)	0.0000 (8)	0.0077 (8)	−0.0021 (8)
C15	0.0234 (13)	0.0168 (13)	0.0201 (15)	0.0026 (11)	0.0037 (11)	0.0033 (11)
O16	0.0247 (9)	0.0213 (10)	0.0199 (11)	0.0029 (8)	0.0026 (8)	0.0004 (8)
O17	0.0259 (9)	0.0188 (9)	0.0219 (10)	0.0049 (8)	0.0045 (8)	0.0015 (8)
O21	0.0256 (10)	0.0243 (10)	0.0247 (12)	0.0023 (8)	0.0052 (9)	0.0044 (8)
O22	0.0281 (10)	0.0219 (10)	0.0294 (12)	−0.0021 (9)	0.0075 (9)	0.0061 (9)
O23	0.0320 (11)	0.0267 (11)	0.0305 (13)	−0.0006 (9)	0.0081 (10)	0.0006 (9)
O24	0.0223 (9)	0.0233 (10)	0.0372 (13)	−0.0016 (9)	0.0025 (9)	0.0020 (9)
O25	0.0293 (11)	0.0330 (12)	0.0358 (13)	−0.0115 (9)	0.0135 (10)	−0.0143 (10)

Geometric parameters (Å, º)

Na1—O25	2.305 (2)	C5—C15	1.516 (4)
Na1—O8^i	2.342 (2)	C5—H5	1.0000
Na1—O11	2.357 (2)	C6—O7	1.242 (3)
Na1—O1^i	2.463 (2)	C6—O8	1.258 (3)
Na1—O14	2.551 (2)	O7—Na3^viii	2.295 (2)
Na1—O16^i	2.588 (2)	O8—Na4^viii	2.303 (2)
Na2—O14^ii	2.391 (2)	O8—Na1^viii	2.342 (2)
Na2—O14	2.426 (2)	C9—O10	1.254 (3)
Na2—O16^iii	2.447 (2)	C9—O11	1.258 (3)
Na2—O21^iv	2.481 (2)	O10—Na3^viii	2.409 (2)
Na2—O21^v	2.503 (2)	O11—Na4^ix	2.326 (2)
Na2—O25	2.596 (3)	C12—O13	1.239 (3)
Na3—O7^i	2.295 (2)	C12—O14	1.257 (3)
Na3—O24^iii	2.365 (2)	O14—Na2^ii	2.391 (2)
Na3—O22^vi	2.397 (2)	C15—O16	1.251 (3)
Na3—O10^i	2.409 (2)	C15—O17	1.270 (3)
Na3—O24^vi	2.429 (2)	O16—Na2^iv	2.447 (2)
Na3—O23^vi	2.480 (2)	O16—Na4^iv	2.483 (2)
Na4—O8^i	2.303 (2)	O16—Na1^viii	2.588 (2)
Na4—O11^vii	2.326 (2)	O21—Na2^iii	2.481 (2)
Na4—O13	2.332 (2)	O21—Na2^x	2.503 (2)
Na4—O22	2.378 (2)	O21—H21A	0.87 (3)
Na4—O16^iii	2.483 (2)	O21—H21B	0.79 (3)
O1—C2	1.430 (3)	O22—Na3^vi	2.397 (2)
O1—C5	1.434 (3)	O22—H22A	0.83 (3)
O1—Na1^viii	2.463 (2)	O22—H22B	0.82 (3)
C2—C6	1.521 (4)	O23—Na3^vi	2.480 (2)
C2—C3	1.531 (4)	O23—H23A	0.96 (4)
C2—H2	1.0000	O23—H23B	0.68 (3)
C3—C9	1.543 (4)	O24—Na3^iv	2.365 (2)
C3—C4	1.574 (4)	O24—Na3^vi	2.429 (2)
C3—H3	1.0000	O24—H24A	0.78 (3)
C4—C5	1.536 (4)	O24—H24B	0.81 (3)
C4—C12	1.548 (4)	O25—H25A	0.67 (3)
C4—H4	1.0000	O25—H25B	0.88 (4)
O25—Na1—O8^i	97.89 (8)	C5—C4—H4	109.2
O25—Na1—O11	152.77 (9)	C12—C4—H4	109.2
O8^i—Na1—O11	104.02 (7)	C3—C4—H4	109.2
O25—Na1—O1^i	102.63 (8)	O1—C5—C15	109.0 (2)
O8^i—Na1—O1^i	65.78 (7)	O1—C5—C4	106.2 (2)
O11—Na1—O1^i	101.02 (7)	C15—C5—C4	113.5 (2)
O25—Na1—O14	80.96 (8)	O1—C5—H5	109.3
O8^i—Na1—O14	104.47 (7)	C15—C5—H5	109.3
O11—Na1—O14	78.07 (7)	C4—C5—H5	109.3
O1^i—Na1—O14	169.85 (8)	O7—C6—O8	125.9 (2)
O25—Na1—O16^i	95.85 (8)	O7—C6—C2	116.1 (2)
O8^i—Na1—O16^i	128.01 (8)	O8—C6—C2	118.0 (2)
O11—Na1—O16^i	83.33 (7)	C6—O7—Na3^viii	135.08 (18)
O1^i—Na1—O16^i	62.32 (6)	C6—O8—Na4^viii	125.98 (17)
O14—Na1—O16^i	127.16 (7)	C6—O8—Na1^viii	123.86 (17)
O14^ii—Na2—O14	89.28 (7)	Na4^viii—O8—Na1^viii	105.73 (8)
O14^ii—Na2—O16^iii	150.92 (7)	O10—C9—O11	124.6 (3)
O14—Na2—O16^iii	107.94 (7)	O10—C9—C3	120.2 (2)
O14^ii—Na2—O21^iv	112.17 (8)	O11—C9—C3	115.2 (2)
O14—Na2—O21^iv	83.25 (7)	C9—O10—Na3^viii	129.23 (18)
O16^iii—Na2—O21^iv	93.41 (7)	C9—O11—Na4^ix	118.40 (15)
O14^ii—Na2—O21^v	84.27 (7)	C9—O11—Na1	138.11 (16)
O14—Na2—O21^v	152.37 (8)	Na4^ix—O11—Na1	91.74 (7)
O16^iii—Na2—O21^v	89.81 (7)	O13—C12—O14	124.9 (2)
O21^iv—Na2—O21^v	74.50 (8)	O13—C12—C4	118.6 (2)
O14^ii—Na2—O25	83.31 (7)	O14—C12—C4	116.4 (2)
O14—Na2—O25	77.85 (7)	O13—C12—Na1	89.43 (16)
O16^iii—Na2—O25	77.91 (7)	O14—C12—Na1	56.33 (13)
O21^iv—Na2—O25	155.47 (8)	C4—C12—Na1	125.56 (16)
O21^v—Na2—O25	127.66 (7)	C12—O13—Na4	133.31 (17)
O7^i—Na3—O24^iii	93.08 (8)	C12—O14—Na2^ii	133.19 (18)
O7^i—Na3—O22^vi	92.03 (8)	C12—O14—Na2	127.18 (16)
O24^iii—Na3—O22^vi	84.94 (8)	Na2^ii—O14—Na2	90.72 (7)
O7^i—Na3—O10^i	86.01 (7)	C12—O14—Na1	99.47 (15)
O24^iii—Na3—O10^i	93.92 (8)	Na2^ii—O14—Na1	103.17 (7)
O22^vi—Na3—O10^i	177.68 (8)	Na2—O14—Na1	95.62 (7)
O7^i—Na3—O24^vi	174.60 (8)	O16—C15—O17	125.9 (2)
O24^iii—Na3—O24^vi	85.48 (8)	O16—C15—C5	119.6 (2)
O22^vi—Na3—O24^vi	93.02 (8)	O17—C15—C5	114.5 (2)
O10^i—Na3—O24^vi	88.90 (8)	C15—O16—Na2^iv	128.23 (15)
O7^i—Na3—O23^vi	99.97 (8)	C15—O16—Na4^iv	114.27 (16)
O24^iii—Na3—O23^vi	166.82 (9)	Na2^iv—O16—Na4^iv	97.15 (7)
O22^vi—Na3—O23^vi	96.34 (8)	C15—O16—Na1^viii	113.63 (15)
O10^i—Na3—O23^vi	85.23 (7)	Na2^iv—O16—Na1^viii	110.00 (8)
O24^vi—Na3—O23^vi	81.36 (8)	Na4^iv—O16—Na1^viii	83.03 (6)
O8^i—Na4—O11^vii	172.00 (8)	Na2^iii—O21—Na2^x	105.50 (8)
O8^i—Na4—O13	88.15 (7)	Na2^iii—O21—H21A	98 (2)
O11^vii—Na4—O13	87.19 (8)	Na2^x—O21—H21A	107 (2)
O8^i—Na4—O22	81.02 (8)	Na2^iii—O21—H21B	111 (2)
O11^vii—Na4—O22	106.93 (8)	Na2^x—O21—H21B	128 (2)
O13—Na4—O22	118.62 (8)	H21A—O21—H21B	103 (3)
O8^i—Na4—O16^iii	89.47 (7)	Na4—O22—Na3^vi	111.48 (9)
O11^vii—Na4—O16^iii	86.32 (7)	Na4—O22—H22A	114 (2)
O13—Na4—O16^iii	112.66 (7)	Na3^vi—O22—H22A	113 (2)
O22—Na4—O16^iii	127.30 (8)	Na4—O22—H22B	94 (2)
C2—O1—C5	105.96 (19)	Na3^vi—O22—H22B	114 (2)
C2—O1—Na1^viii	116.22 (15)	H22A—O22—H22B	109 (3)
C5—O1—Na1^viii	117.66 (15)	Na3^vi—O23—H23A	109.3 (18)
O1—C2—C6	109.7 (2)	Na3^vi—O23—H23B	102 (3)
O1—C2—C3	105.8 (2)	H23A—O23—H23B	98 (3)
C6—C2—C3	110.8 (2)	Na3^iv—O24—Na3^vi	94.52 (8)
O1—C2—H2	110.1	Na3^iv—O24—H24A	128 (2)
C6—C2—H2	110.1	Na3^vi—O24—H24A	104 (2)
C3—C2—H2	110.1	Na3^iv—O24—H24B	117 (2)
C2—C3—C9	114.9 (2)	Na3^vi—O24—H24B	118 (2)
C2—C3—C4	104.6 (2)	H24A—O24—H24B	96 (3)
C9—C3—C4	114.8 (2)	Na1—O25—Na2	97.47 (8)
C2—C3—H3	107.4	Na1—O25—H25A	122 (3)
C9—C3—H3	107.4	Na2—O25—H25A	120 (3)
C4—C3—H3	107.4	Na1—O25—H25B	118.1 (19)
C5—C4—C12	113.2 (2)	Na2—O25—H25B	88 (2)
C5—C4—C3	102.3 (2)	H25A—O25—H25B	107 (3)
C12—C4—C3	113.5 (2)
O1—C2—C3—C4	20.1 (3)	C12—C4—C5—C15	92.5 (3)
C2—C3—C4—C5	3.0 (3)	O7—C6—C2—C3	73.7 (3)
C3—C4—C5—O1	−25.2 (3)	O17—C15—C5—C4	−60.1 (3)
C4—C5—O1—C2	39.7 (3)	O10—C9—C3—C2	1.3 (3)
C6—C2—C3—C9	−94.3 (3)	O13—C12—C4—C5	45.4 (3)
C9—C3—C4—C12	−1.5 (3)

Symmetry codes: (i) x, −y+2, z−1/2; (ii) −x+1/2, −y+3/2, −z+1; (iii) x, −y+1, z−1/2; (iv) x, −y+1, z+1/2; (v) −x+1/2, y−1/2, −z+1/2; (vi) −x, y, −z+1/2; (vii) x, y−1, z; (viii) x, −y+2, z+1/2; (ix) x, y+1, z; (x) −x+1/2, y+1/2, −z+1/2.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O21—H21A···O11^i	0.87 (3)	1.94 (3)	2.805 (3)	176 (3)
O21—H21B···O17^iii	0.79 (3)	2.16 (3)	2.943 (3)	169 (3)
O22—H22A···O23^vii	0.83 (3)	2.08 (3)	2.845 (3)	154 (3)
O22—H22B···O7^i	0.82 (3)	1.96 (3)	2.730 (3)	157 (3)
O23—H23A···O10	0.96 (4)	1.74 (4)	2.702 (3)	174 (3)
O23—H23B···O8^i	0.68 (3)	2.28 (4)	2.948 (3)	169 (4)
O24—H24A···O10	0.78 (3)	2.36 (3)	3.010 (3)	142 (3)
O24—H24B···O13	0.81 (3)	1.93 (3)	2.740 (3)	176 (3)
O25—H25A···O17^ii	0.67 (3)	2.15 (3)	2.817 (3)	171 (4)
O25—H25B···O17^iii	0.88 (4)	1.82 (4)	2.699 (3)	175 (3)

Symmetry codes: (i) x, −y+2, z−1/2; (ii) −x+1/2, −y+3/2, −z+1; (iii) x, −y+1, z−1/2; (vii) x, y−1, z.